Normal Subgroups and Quotient Groups · Medium problem

In $D_8$ (order $16$), let $H = \langle s\rangle$ (order $2$, a reflection, not normal) and $N = \langle r^2\rangle$ (order $4$, normal). Using $|HN| = \dfrac{|H||N|}{|H\cap N|}$, what is $|HN|$?