Submanifolds of homogeneous spaces are homogeneous

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Is a submanifold of a homogeneous manifold is homogeneous? i.e $X=G/H$ for a Lie group $G$ and a closed subgroup $H$, then if $Y$ is a submanifold of $X$. Is there a subgroup $K$ of $G$ s.t $Y=K/(K\cap H)$?