Show that the space G/H is regular

Question

I need to show that if $G$ is a regular Hausdorff topological group and $H \subset G$ is a closed subgroup, then G/H is also regular.

I was able to prove that the space G/H is Hausdorff, but I am stucked in showing that it is regular, i.e. that we can separate closed sets from points.

Any hints are appreciated,

Thanks