We consider a preemption game between groups, where one of the members of the group can take a costly action on behalf of his group. We describe the equilibrium solution of this problem if players differ in their own costs of action, and if these costs are the players' private information. The equilibrium is typically characterized by delay. The nature of the equilibrium depends on key parameters such as the number of groups and their size. More competition between groups reduces delay, whereas larger groups make members of a given cost type more reluctant to act but may lead to earlier resolution of the conflict between the groups.