A hereditary monarchy of Luminai rules the Dominion. In addition to the emperor, the seven Great Houses of the Luminai hold a great deal of financial, political, and religious clout. Though all Dominion citizens are loyal to the emperor, many Cassian humans are just as loyal to the Great House with which they are affiliated.
Beyond the nobility, however, the Dominion government has proven to have a surprisingly efficient and resilient power structure. The Dominion way of doing things is orderly, organized, and run like a complex but well-run machine. When the Dominion sets about to do something - whether it's building public works, creating and financing the military, or creating temples - they do it with organization, discipline, and pride.
On Nexus and other worlds of the empire, the Dominion appoints governors to rule over their territories. These governors are almost always Luminai - though some Fringe worlds have made do with highborn Cassians - and generally have a fairly close relationship to the emperor's court. Governors out of favor with the emperor invariably find themselves removed from office, sometimes forcibly.
All territorial governors levy taxes on their citizens, but these are almost never excessive, and are generally paid without complaint. The contract between a governor and his lowborn and highborn citizens is a sacred trust that serves as the foundation of the empire's success. The Dominion cannot survive without the hard work and loyalty of its citizens, and those same citizens understand that the protections and privileges of the empire come at a price.