Take 3 planes in $\mathbb{C}^4$ (or equivalently 3 points in the Grassmannian Gr(2,4)). What is the subgroup of SL(4) (with the obvious action on $\mathbb{C}^4$) that leaves the 3 planes invariants?
If the 3 planes are in generic positions it should be isomorphic to SL(2), what happens for special configurations of the 3 planes?