The orbit map is open

Question

Let a locally compact second countable Hausdorff Group $G$ acting continuously and transitively on a locally compact second countable Hausdorff topological space $X$ and let $y$ be an element in $X$ and let $H$ be the stabilizer of $y$ in $G$ and $G/H$ be regarded as a topological space with the quotient topology and let $f:G/H \to X$ by: $f(g*H)=g*y$ . I need to show that $f$ is open. Could someone can give me help to prove that $f$ is open?