  Recent experiments have explored two-dimensional electron gases (2DEGs) at
oxide (111) surfaces and interfaces, finding evidence for hexagonal symmetry
breaking in SrTiO$_3$ at low temperature. We discuss many-body instabilities of
such (111) 2DEGs, incorporating multiorbital interactions in the $t_{2g}$
manifold which can induce diverse magnetic and orbital orders. Such broken
symmetries may partly account for the observed nematicity, cooperating or
competing with phonon mechanisms. We present an effective field theory for the
interplay of magnetism and nematic charge order, and discuss implications of
the nematicity for transport and superconductivity in (111) 2DEGs.
