First I don't really like the idea of group quests, they just separate the player base in people who can and can't do them and feel so MMO-like "You must play together now, join a guild, dammit"
But ok, if you must:
1) The best way to make a group necessary is a bunker with a door you only can open when 2,3,4... switches are thrown simultaneously. Or pressure plates. Apart from just digging through a single player can do these quests as well if you drop the "simultaneous" requirement.
2) The group stands before 3 doors that open to 3 rooms. When the doors open, a voice says "Self destruct sequence commencing. 99, 98... In each room is part of the puzzle to deactivate the sequence, for example in one room the handbook, the next room has an access to the energy generator through a maze of rooms and the last room has a map of the installation. If they don't succeed, all the cool stuff in the bunker is destroyed by the explosion
3) Instead of a self destruct of a bunker this could also be an ICBM launch bunker. You would accidentally reactivate the start sequence of a rocket but the lid is still closed. If you don't turn it off, the rocket will explode inside and destroy the valuable loot as well.