I was thinking about some sects/political factions/usurpers/other madmen. Like a faction that believes the empire should be dissolved and the Terrans should come under the rule of the alien hive's queen. Or a faction that has a "better emperor" (it's all lies of course, only the player is the best and the rightful emperor capable of saving the human race!)

I'm sorry, but this made me think of The Borg. However there have been human groups I suppose that sort of function in this way. Consider the rise of Mao and the Cultural Revolution in China. It was definitely a single minded mentality when the Communists decided to take over. So it does sound like you are saying that you want these guys to be strict baddies, getting the hate of all who are loyal. This is probably because the Emperor is sort of the player character. In that way, their goal could just be to wreak havoc. Then again, that's boring. So maybe putting their man and their way of thinking on the throne and the people is the end-game here. Which, considering that these are bad guys and not freedom fighters, makes sense. This may be an idiot question, but what is your Emperor like? Is his character shaped by the player? Just wondering.

Hmmm, maybe let's forget about the "terrorists" parts for now. And think about some group inside the empire that opposes the Emperor.

What would they want? How they are named? Who supports them and why?

This may be an idiot question, but what is your Emperor like? Is his character shaped by the player? Just wondering.

No... The Emperor is not represented and is most likely not a character at all, it's just the player. Like in basicly all strategies (civilization, all 4X, etc).

In short the emperor IS YOU :) So obviously he/she is the most smart, competent and up to the job person that was even born in the whole universe :)

(how glad I am I can count on natural player's megalomania here, no player will question how marvelous and natural born leader the Emperor is :))

So is this kind of like a Tropico 4 type game where you have your malevolent ruler and the player is basically in charge of what happens in the universe? However the Emperor is not really a player character but merely a representative character? If this is the case, then the usurper situation or the baddies trying to take out the pathetic infidels might be a good way to go.

They might be like "Rebel Alliance of Star Wars" or "Barbarians of Civilization" depending on your purpose. It might even be related to how Emperor treats people, rebel fighters if you're harsh, evil ones if you're benevolent.

You can have it be an impromptu alliance of sorts. A good theme could be that when pushed by a large enemy, even unsuspecting allies emerge. Not all of your opponents are self-interested but a few are, that's the nature of an alliance of necessity.

You can have terrorists turn coat on each other for you as well by this logic.

Ships can have run around bureaucracy. With one man attempting to control large swathes of territory there is bound to be a bureaucratic problem. They might have paid off a few people in your cabinet.

They also attract other prospective emperor investments from elsewhere. Ultimately they can be portrayed as a ragtag bunch consisting of ideologues, actual criminals, and those who want to succeed YOU. The power here is that you kill them all the same.

I dunno, this sound good?