I know the special orthogonal group $SO(6)$ can be decomposed into $SU(3)$ (it's a singlet plus an adjoint rep of $SU(3)$ if I remember correctly?).
More generally $SO(2N)$ can be decomposed into $SU(N)$. I'm looking for something that can be applied to the indefinite orthogonal group I'm working with, the specific case for me being $SO(4, 2)$ to $SU(3)$
For starters here, I know that $SO(4, 2; R)$ is contained within $SO(6,C)$ but that's about as far as I've gotten.
Any references to papers or just a good pointer in the right direction would be much appreciated. A full answer would of course be awesome too!