Psl(2,q) quotients of some hyperbolic tetrahedral and coxeter groups

We classify quotients of type PSL(2,q) and PGL(2,q) with torsion-free kernel for four of the nine hyperbolic tetrahedral groups. Using this result, we give a classification of the quotients with torsion-free kernel of type PSL(2q) ×Z₂ of the associated Coxeter or reflection groups. These do not admit quotients of type PSL(2,q),PGL(2,q). We also study quotients of type PSL(2,q) and PGL(2,q) of the fundamental group of the hyperbolic 3-orbifold of minimal known volume.