  We classify plane curves $\mathcal{C}$ possessing two Galois points $P_1$ and
$P_2 \in \mathbb{P}^2 \setminus \mathcal{C}$ such that the associated Galois
groups $G_{P_1}$ and $G_{P_2}$ generate the semidirect product $G_{P_1}\rtimes
G_{P_2}$. New examples of plane curves with two Galois points are also
presented.
