Peter, depending on the ship, there are limited numbers of connecting cabins, like a double connecting to a triple. Newer ships have family cabins that can sleep 8, or even larger, multi-bedroom suites.
Some cruise lines allow under-21s only in a connecting cabin, while others allow adjacent and the occasional across-the-hall room.
Many cruise lines don't have group rates per se, but have other perks for a group of at least 8 cabins (in most cases). I'd advise you to seek out an experienced group cruise travel agent who can advise you of all the perks, options, etc.