Normal Subgroups and Quotient Groups · Medium problem

In $S_4$, let $H = \langle(1\,2)\rangle$ (order $2$) and $N = A_4$ (order $12$, normal in $S_4$). Using the Second Isomorphism Theorem relation $|HN| = \dfrac{|H||N|}{|H\cap N|}$, what is $|HN|$?