Let $\pi: G \rightarrow S$ be a finite flat group scheme over a locally noetherian connected base scheme $S$. Its degree is defined as the rank of the locally free $\mathcal O_S$-module $\pi_* \mathcal O_G$. Let $H \subset G$ be a closed subgroup scheme of $G$ which is also finite flat over $S$.

I want to show that the degree of $H$ divides the degree of $G$. How does one do this? I guess this must be easy but I'm somehow stuck.