Found a resource for you, the Order of the Golden Dawn didn’t exist at the time, but here is a page with a lot of organizations of the time History of the Order of the Golden Dawn. The Freemasons are the most likely, though they were not all that secretive, they were a public men’s club, even though just as they do today, their inner workings are shrouded in mystery. This should boost your ideas, the rest sounds absolutely awesome though.