Order of the Eye
Order of the Hour
The Order of the Hour is a knightly order founded to protect the Akatosh Chantry and the Cathedral of Akatosh. The order has its own hierarchy but also falls under the control of the Primate of Kvatch.
Order of the New Moon
The Order of the New Moon is a Khajiit Dragon cult that worships a Dragon named Laatvulon. They are also dedicated to raising Laatvulon's master, Kaalgrontiid, into the Dark Eon, and shift their worship to Kaalgrontiid after Laatvulon's death.
Ordinators are the holy guards of the Tribunal Temple. They enforce Temple law across the whole of Morrowind and have authority over almost every organization. They are typically recruited from House Indoril, with their influence especially seen in their armor style. The Hands of Almalexia are an elite subset of Ordinators, chosen to serve the living goddess Almalexia.
Outlaws are a group of bandits found in the Inner Sea Armature and sometimes Deadhollow Halls. They can also be encountered in Chid-Moska Ruins, though this groups has nothing in common bar the name, and they will soon be deprecated in Update 19.