Hey everyone,

I have an exercise in which I need to show the subgroup $\displaystyle H \subset S_4$ is normal, when $\displaystyle H$ is given as:

$\displaystyle H = \lbrace e, (12)(34),(13)(24),(14)(23) \rbrace$

I've maneged to show $\displaystyle H$ is indeed a subgroup and my idea is to somehow use the conjugate of a subgroup, but can't seem to make it work. Is there a better way to tackle this problem?

Thanks in advance.