I'm trying to figure out how a homogeneous space is built, and I know the theorem below:
Theorem: Let $G$ be a Lie group, and $H$ closed normal subgroup of $G$. Then the cosets space $G/H$ with the induced group structure is a Lie group.
My question is " what would be Lie algebra of $G/H$, and its vector fields associated flows if $H$ had only uniform (discrete) subgroup instead of closed normal subgroup.
(Remark: A subgroup $A$ of $G$ is called a uniform subgroup If $G/H$ is compact.)
Any help will be appreciated, thanks in advance.