The maximal discrete extension of $S{L}_2({\mathcal{O}}_K)$ for an imaginary-quadratic number field $K$

Let ${\mathcal{O}}_K$ be the ring of integers of an imaginary quadratic number field $K$. In this paper we give a new description of the maximal discrete extension of the group $S{L}_2({\mathcal{O}}_K)$ inside $S{L}_2(\mathbb{C})$, which uses generalized Atkin-Lehner involutions. Moreover we find a natural characterization of this group in $SO(1,3)$.