  We classify the compact quantum groups acting on 4 points. These are the
quantum subgroups of the quantum permutation group $\mathcal Q_4$. Our main
tool is a new presentation for the algebra $\rm C(\mathcal Q_4)$, corresponding
to an isomorphism of type $\mathcal Q_4\simeq SO_{-1}(3)$. The quantum
subgroups of $\mathcal Q_4$ are subject to a McKay type correspondence, that we
describe at the level of algebraic invariants.
