  We investigate 3-nondegenerate CR structures in the lowest possible dimension
7 and show that 8 is the maximal dimension for the Lie algebra of symmetries of
such structures. The next possible symmetry dimension is 6, and for the
automorphism groups the dimension 7 is also realizable. This part (II) is
devoted to the case where the symmetry algebra acts intransitively. We use
various methods to bound its dimension and demonstrate the existence of
infinitely many non-equivalent submaximally symmetric models. Summarizing, we
get a stronger form of Beloshapka's conjecture on the symmetry dimension of
hypersurfaces in $\mathbb{C}^4$.
