Let $N,H,L$ be subgroups of a group $G$ such that $N$ is normal in $G$, and $L$ is normal in $H$. By using natural map arguments, show that $(LN)/N$ is normal in $(HN)/N$.
Could any one tell me how to solve this one?
The natural maps are $\phi_1: G\rightarrow G/N(g\mapsto gN)$, $\phi_2:H\rightarrow H/L(h\mapsto hL)$
Well, what to do later?