You're almost there. Dig a little bit deeper and find some extra factions. It's not about Rs vs Ds. It's about good vs evil.

-Ordo Rosae Crucis (or 'How to be a magician without practicing magic')

-IOOF (ancient)

-Temple of Set (evil -- Aquino)

-Ordo Templi Orientis (Crowley thought he was John Dee)

-Thule Society (they're still around)

-Knights Templar (they're still around too -- the Cathars carry the traditions in Languedoc)

-Asian secret societies (I'm not as familiar with these, as all my experience has been in western secret societies)

-And many more -- some walk the right hand path, some walk the left hand path, and some walk the middle path

This battle is bigger than the US and has raged on for thousands of years. Even in ancient Egypt, some worshipped Osiris, while others worshipped Set. Darkness may creep in, but Sol Invictus conquers it every morning.