In computer networks, multicast models a class of data dissemination applications, where a common data item is routed to multiple receivers simultaneously. The routing of multicast flows across the network may incur a cost, and such a cost is to be recovered from payments by receivers who enjoy the multicast service. In reality, a group of potential multicast receivers exist at different network locations. Each receiver has a valuation for receiving the multicast service, but such valuation is private information known to itself. A multicast scheme asks each potential receiver to report her valuation, then decides which subset of potential receivers to serve, how to route the multicast flow to them, and how much to charge each of them. A multicast scheme is stragegyproof if no receiver has incentive to lie about her true valuation. It is further group strategyproof if no group of colluding receivers has incentive to lie. We study multicast schemes that target group strategyproofness, in both directed and undirected networks. Our main results reveal that under group strategyproofness, a compromise is necessary in either routing optimality or budget balance. We also design multicast schemes that pursue maximum budget balance while guaranteeing group stragetyproofness and routing optimality.