Let G = $U(14) \times Q$ where $U(14)$ is the multiplication modulo $14$ group and $Q$ is the quaternion group. Let $N = \langle(9,j)\rangle$. Find $G/N$.
I calculated that $\langle(9,j)\rangle$ is $\{(9,j),(11,-1),(1,1)\}$ but don't know how to proceed. Will $G/N$ be the group consisting of all $16$ cosets, considering $U(14) \times Q$ is of order $48$ and $N$ is of order $3$? Any help would be greatly appreciated.