  We perform a numerical study of the phase diagram of the model proposed in
\cite{Shifman:2012vv}, which is a simple model containing non-Abelian vortices.
As per the case of Abrikosov vortices, we map out a region of parameter space
in which the system prefers the formation of vortices in ordered lattice
structures. These are generalizations of Abrikosov vortex lattices with extra
orientational moduli in the vortex cores. At sufficiently large lattice spacing
the low energy theory is described by a sum of $CP(1)$ theories, each located
on a vortex site. As the lattice spacing becomes smaller, when the
self-interaction of the orientational field becomes relevant, only an overall
rotation in internal space survives.
