I'm trying to find an example when G is a lie group that admits a bi invariant riemannian metric and H a is closed subgroup wich the manifold G/H does not admit a G-invariant riemannian metric.

I know so far that if G/H admits a invariant Riemannian metric, then H has to be compact. So I'm searching for a lie group G that admits a bi invariant riemannian metric and H a closed subgroup that is not compact, this will solve the problem. Does anyone know such group?

Thank you for any help!