  We derive explicit isomorphisms between certain congruence subgroups of the
Siegel modular group, the Hermitian modular group over an arbitrary
imaginary-quadratic number field and the modular group over the Hurwitz
quaternions of degree 2 and the discriminant kernels of special orthogonal
groups SO 0 (2, n), n = 3, 4, 6. The proof is based on an application of linear
algebra adapted to the number theoretical needs.
