You missed the point. No one said that all of these people were playing at one time. These were the number of people in the group. You start with a number of peoples. Some of them leave, some new ones join. Not everyone shows up every week (or month). Since it was a total number of people game with, it is people you started with plus anyone who joined.
So post up your numbers. How many groups and how many people in each group.
And actually, you can quite easily keep your players in groups greater than six fairly engaged. There a couple of techniques to actually do it easily, unless you are a GMing control freak.
1) Designated NPC: Give the Player some instructions about what is going on, the purpose of the scene they are about to be in, and what they should, ideally be providing for the PC/ just a nudge about what to do, and they can play the scene out without you. They can post-game the scene with you right after, at the end of the game, or via notebook/email/ etc. They gain experience, that they can apply to any of their characters (some players just assign them to their designated NPC).
These technique allows you to provide a more engaging scene for the PC, allowing you the GM to work with other players and their scenes or set up other scenes with PCs and designated NPCs. This can streamline your game and provide "fun" for everyone.
1b) Assigned Monsters: Related to above, is this sub category. Well there is often something that needs to be bashed, and unless your players are in a dungeon or artificially shoved together at all times, someone is not going to be there. They would be bored watching this combat. Assign them monsters, give them a little direction, and watch your PCs start to sweat, as the mooks now are "dangerous" as they have more tricks and tactics than you as a singple player/GM can provide.
1c) Auxillary GM: Have a rules lawyer, put him to work on your side of things. Have him run the rules while you work the story. If your game has complicated rules for magic (Chivalry and Sorcerry), Combat, Trade (Traveller), or so on, having someone simply dedicated to running that aspect of the game can free you, the GM to running the campaign.
2) NPC Troupe: A player has NPCs that revolve around them. These are family, friends, coworkers, neighbors, girlfriends, bosses, the girls at the market that you always talk to, the two guys at the coffee shop that they always stop at, and so on. These NPCs provide versimiltude for the character and connect them to their game world. By assigning Players to various roles, the players can have the troupe of NPCs orbit around them. This frees up the GMs to do other things, provides fresh play for the supporting cast, and keeps people engaged into the world.
3) Acting for your fellow players: Get your players Your players are performing each other. If you tie a bonus exp reward to it, you can get your players really into playing a scene to the hilt. Thus players will often want to pay attention to see who gets the bonus eps that the players will vote on at the end of the game. (If you didn't pay attention to others there was no way they might vote for you.) Anything that gets your players involved with the game is a good thing.
4) Storytelling: This is your ability to engage people with your story telling prowess. The same skills that kept people enraptured around the campfire have a place in the modern Game Masters Arsenel. When I am prepped and warmed up, I can keep them engaged. This worked when I was running a bunch of kids back in the day when actually having a story was the "new" and "innovative" approach to gaming, and it works now.
5) Good GMing techniques. Well I got dozens of them. Running Tactical Scenes at Lightning Speeds with Many Players is one set I used. They are things I had to develop because I did run somewhere between five to ten players at a given time.
No matter how you are doing it, keeping the players engaged and enjoying the game, is the game master job one.
