Now that you've had a number of people tell you how a large group should not be a problem, let me give you some advise on how to solve your large group problem. I have had to cut players before, due to games being too large, so perhaps I can help. First I'll recommend how to pick people to keep/cut, then some advise on how to do it.
* First and foremost, cut any problem players. It sounds like you already did this.
* Cut anyone who misses a lot of games. They're not really contributing.
* Make a list of who is contributing the most to the game. These are people you're going to want to keep.
* Think about logistics and supplies: Is the game at someone's house? Does one player have all the rule books? Is one person bringing miniatures? Does one person always bring snacks to share? Does one player give others a ride? These are probably important people to keep.
* Who has been with you the longest? These are probably also people you want to keep.
Deciding who to cut, assuming you don't have problem players, is always hard. It's no fun telling your friend that you can't have them around. The trick is make sure you don't make them feel like you don't want them around.
Once you've decided, it's about breaking the news. Sometimes, it's really easy. "Dude, I'm sorry, but you're always late and miss half the sessions. I just won't put up with it anymore." (I've had to use that before.) If you have good players, but it's all about the logistics of the room, then it gets harder.
Make sure you let everyone know WHY you're cutting down the group size. Do not cite the player who demanded it, or he will be the bad guy. Just say that with club rules saying that you should have 4-6 and with the logistics of the room, it's time to reduce the group size down to no more than 6.
If you have everyone's e-mail, ask for any volunteers. Actually, ask if anyone wants to run another game for those players still seeking a game. That would be a quick fix and get more people playing in the long run.
When you do cut the person, tell them directly and let them know why they got cut. Treat them like a mature individual. You'll want to let the rest of the group know too, just so there are no misunderstandings. Do this outside of the normal game. This will help avoid disruption.
If you really can't decide, you can draw names from a hat if you really must. I've cut people from a number of groups over the years and have never had to resort to this, but then I'm a cynical jerk who can always find some reason to cut people.
And my final bit of advise, in case you are someone who does not like social confrontation: Decide who you're going to cut. Tell everyone that you're going to do it randomly. Make sure the chosen person loses. Heck, put names in a hat and have someone else draw. Just make sure that the person in question is the only name in the hat, then destroy the other slips quickly so no one can find out. You can also print up multiple name lists of the whole group, with that person as each number on different lists. Then have someone else roll. Just pull out the correct list and close your folder.
You might even want to have someone else in the club roll or draw, just to make it "fair".
Is it kind of a lousy thing to do? Yes. It might count as the lesser of two evils however. It saves on hurt feelings and avoids drama. It requires you to be a sneaky bastard, but then you are a DM, aren't you?
I take no responsibility if this backfires on you, however. You have to be the best sneaky bastard.
And, yes, I have used the list method. I just didn't show anyone the list.