I think there is a much mistaken idea about much of the history of collegiate groups. Many seem to think that their society was founded as "secret societies" and then later added terms like fraternity, or sorority......
The idea that "Alpha Beta Gamma" or "Philomathean" or "phi beta kappa" whatever the name may be were "secret societies" but in fact none of them ever were. "Secret Societies" are just that.....secret, none knows who the members are, or even knows what the groups real name is.
Any organization founded after Phi Beta kappa are merely "societies with secrets". The Freemasons also consider themselves to no longer be a "secret society" but rather the above, a Society with secrets.
So, ADPi, Phi Mu, Kappas, Thetas, or any other groups really aren't true secret societies.
Just a friendly info tip......