Civilization VI Secret Societies is a game mode that came out with the Ethiopia Pack. It introduced the concept of Secret Societies in the form of governors whose promotions give us powerful bonuses, access to new buildings, units and improvements. We will focus on The Hermetic Order strategies and perks.
The Hermetic Order are unorthodox scientists and alchemists. Strategically they are very underwhelming in comparison to other secret societies. They rely heavily on getting Great Persons in order for Ley Lines (the order's exclusive resource) to be useful. Also they do not receive early game bonuses. The reason to play this Hermetic order is for the fun of seeing tiles with really high yields of all types in the Industrial Era.
Ley Line gives a standard adjacency bonus to all specialty districts.
Reach the Medieval Era
Allows you to construct the Alchemical Society, a powerful replacement of the University.
Reach the Industrial Era
For every Great Person earned, Ley Lines receive +1 yield equal to that Great Person's district type. Great Admirals and Great Generals earn +1 Science.
Reach the Atomic Era
Unlocks Occult Research, a city project that provides Gold while active. When completed, it grants Great People points, and Science for every Ley Line in the city.
The extra Production and Gold is a welcomed bonus. Nevertheless this is not the important part of this building's description. The +1 Great Engineer and +1 Great Merchant points are the main selling points. Recruiting a lot of Great Persons is the most important part of the strategy when playing the Hermetic Order.
The Oracle wonder synergies great with the Alchemical Society, making patronage of Great People cost 25% less Faith and therefore helping your goal of having as much Great People as possible.
Civilizations that enjoy bonuses in regards to Great Persons (such as Kongo, Brazil, Sweden and Scotland) are great with the Hermetic Order, but this building really helps so other Civilizations that do not enjoy bonuses in this area are viable (and sometimes good) with this secret society.
In comparison to the Old God Obelisk (Voidsingers), the Alchemical Society is very lackluster as it requires that you have a Campus district with a library in it. While the Old God Obelisk has no requirements and therefore its bonuses hit much earlier in the game, actually securing or helping you get a victory.
In the same way the Gilded Vault (Owls of Minerva) is also better than the Alchemical Society, but not by much as they do have equivalent bonuses and the former also requires you to have a Harbor and a Commercial Hub in the city to make full use of its bonuses (in which case it is much better). What really makes the difference is that the Owls of Minerva have early game bonuses that helped putting a foot in the game, while the Hermetic Order does not. Therefore being in good shape to build Gilded Vaults is easier.
Ley Lines are a resource exclusive to the Hermetic Order. Making it so only this secret society can see them.
They give standard adjacency bonuses to all Districts. When the Industrial Era is reached and the Hermetic Order's governor is promoted, Ley Line also grants bonus yields whenever a Great Person is earned.
This last bonus is what makes Ley Line the whole point of playing this secret society. For instance:
Upon reaching the Industrial Era and promoting the Hermetic Order's governor you should get something like this. A single tile that yields 20+ (without taking into consideration district adjacency bonuses).
For this reason, tiles with Ley Line become very powerful once the Industrial Era is reached. In the previous eras you should be trying to settle your cities near Ley Line tiles.
TLDR: Don't pick the Hermetic Order if winning is important. Ley Lines are a 0 yields resource until the Industrial Era (unless district adjacency is considered, and then it is still bad). The Hermetic Order lacks in early bonuses, which other secret societies not only do have, but also their bonuses keep being useful throughout the rest of the game.
To meet the Hermetic Order you must discover a Natural wonder. Granted you're not restarting the game in order to get this in turn one (for instance in a multiplayer game), then you have to do a lot of exploring.
Cities must be planned around Ley Lines, a resource whose locations are not revealed until you join the Hermetic Order, therefore you must discover a Natural wonder as soon as possible (hopefully before there are 3 cities in your empire). Producing or purchasing 2 Scouts is recommended.
Once you meet the Hermetic Order and promote its governor you can see Ley Lines. An almost useless resource in this era that actually occupies useful space. This is the reason why the Hermetic Order's early game is so bad when compared to other secret societies. If you want to make some use of Ley Lines, build districts next to them to get a +1 adjacency bonus.
Pingala's 'Grants' promotion makes it so +100% Great People points are generated in the city. This is the most important governor promotion while playing the Hermetic Order because later in the game Ley Lines will have yields based on the amount of Great People you have generated in the game. In the secret societies mode governor titles are easier to get in the early game, everytime you meet a secret society they grant you a governor title.
In the Medieval Era the Hermetic Order gives you access to its exclusive building, the Alchemical Society, which replaces the University. As we explained before the great part of this building's bonuses is that it gives you extra Great Person points, which is the basis of the Ley Lines strategy.
Build as many Alchemical Societies as you can, the idea is not only to catapult yourself into a Science victory but also to get as many Great People as possible. Great Scientists are preferred, patronage with Faith or Gold if possible.
Settle as many cities near Ley Lines as you can.
Once the Industrial Era is reached you get access to Indoctrination Promotion, which in the case of the Hermetic Order makes it so your Ley Lines are finally useful. This is the power-spike for civilizations that chose the Hermetic Order, that is, if there are enough Ley Lines in their territories.
The contradiction while playing the Hermetic Order is that, if you have Ley Lines that have good yields, it means you were getting a lot of Great Persons, and therefore were winning the game anyways (despite having no bonuses from this secret society)
In the Atomic Era you gain access to Occult Research, a city project that provides Gold while active, and once completed it grants Great People points and Science for every Ley Line in the city. In every game I tried this secret society there were not enough Ley Lines to justify this bonus.
Hammer down your science victory. Place spies in your Spaceports as the Owls of Minerva covert operations will sabotage your efforts quite a lot.
The hermetic Order relies on Ley Lines having high yields. Therefore civilizations that produce a lot of Great Persons are best with the Hermetic Order.
Brazil led by Pedro II has a great advantage while competing for Great People. Pedro II's leader agenda is Magnanimous: Recruiting or patronizing a Great Person refunds 20% of their point cost.
The Swedes' civilization ability is Nobel Prize, which grants them +1 Great Scientist and Great Engineer points from Universities and Factories respectively. Also upon recruiting a Great Person this civilization receives +50 Diplomatic Favor, which should be traded with other Civilizations for as much as 400 gold, which in turn should be used towards Patronizing another Great Person, entering a virtuous cycle.
Russia is a religious civilization that has a replacement for Holy Sites, the Lavra provides 1 extra Great Writer, Prophet, Artist and Musician points. Building both Holy Sites and Campuses will make it so Russia can patronize a lot of Great Persons. This civilization works much better with the Voidsingers secret society, but if you're set on playing the Hermetic Order, Russia is one of the better options.
The Scotish must be happy, if they are then they receive bonus Production and Science, and most importantly for this strategy, +1 Great Scientist and +1 Great Engineer points from Campuses and Industrial Zones respectively. Ecstatic cities double these bonuses. Tip: Be the suzerain of Buenos Aires, Bonus resources will behave like Luxury resources, providing 1 Amenity per type.