  We theoretically establish the mean-field phase diagram of a homogeneous
spin-$1$, spin-orbit coupled Bose gas as a function of the spin-dependent
interaction parameter, the Raman coupling strength and the quadratic Zeeman
shift. We find that the interplay between spin-orbit coupling and
spin-dependent interactions leads to the occurrence of ferromagnetic or
ferronematic phases which also break translational symmetry. For weak Raman
coupling, increasing attractive spin-dependent interactions (as in $^{87}$Rb or
$^7$Li) induces a transition from a uniform to a stripe XY ferromagnet (with no
nematic order). For repulsive spin-dependent interactions however (as in
$^{23}$Na), we find a transition from an $XY$ spin spiral phase ($<S_{z} >= 0$
and uniform total density) with uniaxial nematic order, to a biaxial
ferronematic, where the total density, spin vector and nematic director
oscillate in real space. We investigate the stability of these phases against
the quadratic Zeeman effect, which generally tends to favor uniform phases with
either ferromagnetic or nematic order but not both. We discuss the relevance of
our results to ongoing experiments on spin-orbit coupled, spinor Bose gases.
