When we're discussing a secret society, this means they're no longer secret. How we define what is a secret society then?
Proposal: Secret Societies
We can define it as :
That would cover (for example) the [insert country]'s Secret Services, Illuminati, Masonry, Hashashun, and your wife's misterious 5 hour-long bookclub meetings where she doesn't read any books
You might want to consider using the definition given by Wikipedia:
That makes Skull & Bones a good example of a genuine secret society: