1. The problem statement, all variables and given/known data Suppose G is a finite group, which acts transitively on a set X and let H be a normal subgroup of G. Show that the size of the orbits of the action of H on X are of the same size. 2. Relevant equations 3. The attempt at a solution I haven't been able to get very far with this. The only fact I've gotten is that |H(x)| divides |G|, but I am not sure that is even relevant in this case.