Order of the Claw
The Order of the Claw was created by the Lunar Clergy to guard the Do'Krin Monastery and its main relic: the Golden Claw. Its members are also trained in Khajiiti martial arts. Within the lunar clergy there are other orders, including the Order of the Crescent and the Brotherhood of the Fang.
Order of the Eye
The Order of the Hidden Moon
The Order of the Hidden Moon was an ancient Khajiit order dedicated to Azurah, based in what became the Ashen Scar. They were responsible for dealing with the Dro-m'Athra, by using a form of necromancy which would allow the dark spirits to redeem their corrupted souls and to pass through The Crossing. The Moonlight Blade was the special weapon of their order, blessed by Azurah herself.
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 (also called the New Moon Cult) is a Khajiiti Dragon Cult that worships a Dragon named Laatvulon. They are dedicated to helping Laatvulon's master Kaalgrontiid ascend to become a new moon called the Dark Eon, and shift their worship to Kaalgrontiid after Laatvulon's death.
Order of the Waking Flame
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.