  Pyragas time delayed feedback control has proven itself as an effective tool
to non-invasively stabilize periodic solutions. In a number of publications,
this method was adapted to equivariant settings and applied to stabilize
branches of small periodic solutions in systems of symmetrically coupled Landau
oscillators near a Hopf bifurcation point. The form of the control ensures the
non-invasiveness property, hence reducing the problem to finding a set of the
gain matrices, which would guarantee the stabilization. In this paper, we apply
this method to a system of Van der Pol oscillators coupled in a cube-like
configuration leading to $O_4$-equivariance. We discuss group theoretic
restrictions which help to shape our choice of control. Furthermore, we
explicitly describe the domains in the parameter space for which the periodic
solutions are stable.
