Normal Subgroups and Quotient Groups · Hard problem

In $D_6$ (symmetries of a regular hexagon, order $12$), let $N = \langle r^3\rangle = \{e, r^3\}$ (the order-$2$ central rotation). Given that $N \trianglelefteq D_6$, how many elements of the quotient $D_6/N$ have order $2$?