 As opposed to the case with the direct product, a semidirect product of two groups is not, in general, unique; if and are two groups that both contain isomorphic copies of as a normal subgroup and as a subgroup, and both are a semidirect product of and , then it does "not" follow that and are isomorphic because the semidirect product also depends on the choice of an action of on .For example, there are four non-isomorphic groups of order 16 that are semidirect products of and ; in this case, is necessarily a normal subgroup because it has index 2.One of these four semidirect products is the direct product, while the other three are non-abelian groups