Plane curves possessing two outer Galois points

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.