I just reread the intro. Gretchen is definately NOT Cadmus, because it's explicitely stated that she found Cadmus during an excavation.
The story itself is about a meeting between Gretchen, Cooper, Anya, Cadmus and English Ivan in a secret lair below the Society's headquarter. That part is just about the clandestine operations of the society and it becomes pretty clear that Jedza, Basse, McCabe and Maxine are just useful idiots for Gretchen and her cronies, although I think that all of them know that already.
In the last paragraph Cadmus and Gretchen discuss some kind of magical contraption that Gretchen wants to power up, which needs a certain command phrase that she's looking for and which might be the sole reason for the Explorer Society's continued existence. My guess is that she wants to become a tyrant herself, but that's just a gut feeling.