Let $F/K,F'/K'$ be two galois extensions(maybe infinite), $F\subset F',K\subset K'$, is $G(F'/K')\to G(F/K)$ via restriction open map?

Question

$\textbf{Q:}$ Let $F/K,F'/K'$ be two galois extensions(maybe infinite), $F\subset F',K\subset K'$, is $G(F'/K')\to G(F/K)$ via restriction open map? $G(E/F)$ denotes galois group of $E/F$ field extension.

It is clear that $G(F'/K')\to G(F/(F'\cap K))$ is open surjective map. However, it is not clear that $G(F/(F'\cap K))\to G(F'/K')$ is open but it is continuous.