Same way investigators find out anything - they chase clues. Start with what you know. As Moose pointed out, you know two conspirators. You could chase down where they got their aliases from and follow the clues around their names to figure out where the other names originated.

But a good detective would follow every possible lead, not just the names. What can you find out about the two known conspirators? Where do they live? Who are their families? Their friends? Where do they hang out? If they are involved in a conspiracy with these ten other people, it's not just a matter of where they meet (hold their meetings) now. Where did they meet in the first place? Where did the lives of the two known conspirators intersect? Those points of intersection are the likely points in their histories in which the conspiracy was first born, so who were the other people involved with those two individuals at the time?

Find clues and chase them down.

Cheers,
Michelle