So going to the topic I just have a question: does the Confederation have a society / group that is opposed to the way the Liao's rules?
Let's take a look:
The Combine has the Black Dragon society (including the council of gems), The Commonwealth and the Federated Suns had movements for "pure" bloodlines while the Commonwealth also had separatist movements. The Free Worlds League probably doesn't need any mention civil strife seems to be baked into it, most extreme might be the Regulans or even the old Scourge movement. But did House Liao have something homegrown? You could say Free Capella but that was more a pet project from Hanse Davion
The Warrior Houses have, on occasion, been detractors of the Celestial Wisdom despite their supposed loyalty to his or her person above all else. Imarra and Lu Sann in particular have made moves against the incumbent when they felt their actions were detrimental to the state. Ion Rush was instrumental in deposing Romano by helping Candace assassinate her.
Brings to mind the Roman Praetorians, in a way.