What do you consider big?
There are several ongoing games with about 10-12 players. And some more with about 6-8. The problem with total player numbers are that with more players, risk of failures in connecting (or even showing up at the right time) increases exponentially. So you are unlikely to see many games with about 20 or even more players. That would just not work out well, however technically that should be possible.
If you want to join a MP group, I recommend you got to the MP forum and sign up in the thread of a group of your preference.
I very recently started playing MP. It's fun and don't be shy, most groups welcome new players. If you are located in Europe (or somewhere else, but are free to play when it is evening in Europe), I can recommend the World in Conflict series which I joined some weeks ago. Nice guys and imho a rather reasonable ruleset.
If you are new to MP it is advised you play a minor nation for your first game(s) or play coop with an experienced player.