V4 in S4

You might be referring to either of these:


 * Normal Klein four-subgroup of symmetric group:S4: The subgroup comprising the identity element and the three double transpositions in symmetric group:S4. Concretely, it is the subgroup $$\{, (1,2)(3,4), (1,3)(2,4), (1,4)(2,3) \}$$.
 * Non-normal Klein four-subgroups of symmetric group:S4: A conjugacy class of subgroups, each of which is generated by a pair of disjoint transpositions. For instance, the subgroup $$\{, (1,2), (3,4), (1,2)(3,4) \}$$.