Normal subgroup in $G=G_1 \rtimes G_2$

Question

Given $G=G_1 \rtimes G_2$, so that $\rtimes$ is a semi direct product.

(1) Is it always true that $G/G_1=G_2$ as a quotient group?

(2) Are there occasions that $G/G_2$ makes sense?

Answer 1

1. Yes.

2. If and only if $G_2$ is normal (assuming you are identifying $G_2$ with the subgroup $\{e_1\}\rtimes G_2$), thus if and only if the semidirect product is actually a direct product.

Answer 2

To expand, $G/G_2$ always makes sense. It is the set of (left or right, it's a little ambiguous) cosets of $G_2$ in $G$. However, unless $G_2$ is normal it won't be a group, but it will at least have the same size as $G_1$.