Let G be a group, and let H be normal in G. Prove that every subgroups of G/H is of the form K/H, where K is a subgroup of G with $\displaystyle H \subset K$.

My proof so far:

Let $\displaystyle Y:G \rightarrow \frac{G}{H} $ , let X be a subgroup of G/H. By a theorem, $\displaystyle Y^{-1}(X) = \{t \in \frac{G}{H} : Y(t) \in X \} $ is a subgroup of G.

Any help from here?

Thanks.