Let $H$ be a $\sigma-$compact subgroup of locally compact abelian group $G$ such that $G/H$ is $\sigma-$compact. Is $G$ $\sigma-$compact?

Question

Let $H$ be a $\sigma-$compact, closed subgroup of locally compact abelian group $G$ such that $G/H$ is $\sigma-$compact. Is $G$ $\sigma-$compact?