I believe group dining handles reservations for parties that large. If you call 407-wdw-dine, they can put in you in touch with the right people.
Disney is very accomodating to large groups, but I recommend choosing off-peak times or less popular locations for meals and check with group dining right away about how far in advance you can book reservations, then book them THE day they are available, as soon as group dining opens to get your selections. You'd be amazed how quickly things fill up.
And I highly recommend the Hoop Dee Do in a big group. About 16 of us went while we were there for our wedding, and my brother-in-law got called on stage to participate (avoiding a spoiler, for those who know the show, he's a big burly cop and got my favorite part at the end -- my husband and I started laughing the minute he was chosen and the rest of our family thought we were nuts until they found out why!). There's a bunch of audience participation and it's great with a big group because they try to have at least one or two people participate.
The other thing we did that was very helpful to everyone was create an itinerary of everything that was planned, including who was going to what planned events (so if it's a prepaid meal, like the Hoop Dee Do, and someone shows up who didn't say they wanted to go, you can tell 'em, sorry) and times and reservation numbers. That way everyone has the information up front.
Good Luck!
