There are a total of three governing pillars in the Magisterium.
the first is are aristocratic rulers in the Eight Noble Houses who run the empire through Executive power. These dynasties have held power since the early foundations of the country and their influence and history run incredibly deep.
The second pillar is The Senate the governing power under the Noble Houses. While largely ceremonial (as much of the power resides in the Nobility), they govern and have some control over the military (under their Noble's authorization).
The Third and final power is The Church of the Seven the inquisitive and moral backbone State. Seven gods preside over the nation, and the church is the recognized masters of their doctrine.