Given any manifold $ M $ does there exist  $ G $ a Lie group and $ H,\Gamma $ closed subgroups of $ G $ such that 
$$
M \cong \Gamma \slash G/H
$$

I was inspired to ask by this question:  https://mathoverflow.net/questions/89345/example-of-a-manifold-which-is-not-a-homogeneous-space-of-any-lie-group