When you leave a group, there will be an 8 hour waiting/probation period. Once those 8 hours are up, you can join a new group. During the time you are not in a group, you will notice a drop in power. When you join a new group, as long as the new group has the same or better "Group Skills" then your older group has, then you should retain your power. If the new group is lower in level, then it is possible you will lose some power.
~Jib