DeMolay is reasonably well known and only the degreework is secret. I question whether or not it is completely factual, but it was fun when I was a member so I won't complain.
The other societies I am a member of are The Freemasons, The Royal Arch - related to the Masons, and The Loyal Orange Institution in the US (not terribly secret as everything in the ritual is readily found in the Bible). Technically they are all fraternal organizations and not secret orgs, and their core virtues are all, IMHO, excellent standards for men to live their lives by. As such I am not eager to be thrown out of any of them for accidentally revealing something I have taken an oath not to reveal.
Oath keeping is a prety good virtue in most circumstances too. :-)
Layers within layers, within layers . . . . .