A Ministry is a group within the Seers of the Throne, roughly analogous to an Order, save that it serves and is guided by one of the Iron Seals of the Exarchs. They are ruled by Archmages known as Ministers (who, originally, answered to Tetrarchs).
There are no fixed numbers of Ministries, but dozens, ranging from isolated cults run by Ministers who scarcely deserve the title to the four great Archigenitors. The Ministries evolved within the Fallen World, born as small cults, grow into world-spanning conspiracies with mad Ministers at the helm, and die when the world passes them by.
Every Ministry has a specialty, but it is not a job description for its members. A Ministry’s focus does give it an edge when it comes to accomplishing certain tasks, but regardless of ideology, it takes all kinds to rule the world.