The problem is :
Let $H$ be a normal subgroup of $G$ of order $6$.If $f : G \longmapsto G_1$ be an epimorphism of groups such that $H \subseteq ker f$, then show that $G_1$ is also a homomorphic image of $G/H$.
I don't find any route of solving this problem.I don't even understand the significance of the fact that $|H| = 6$.Please help me by giving me a hint at least.Then I will retry it.Thank you in advance.
Hint. Is $gH\mapsto f(g)$ well-defined?