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We investigate 3-nondegenerate CR structures in the lowest possible dimension7 and show that 8 is the maximal dimension for the Lie algebra of symmetries ofsuch structures. The next possible symmetry dimension is 6, and for theautomorphism groups the dimension 7 is also realizable. This part (II) isdevoted to the case where the symmetry algebra acts intransitively. We usevarious methods to bound its dimension and demonstrate the existence ofinfinitely many non-equivalent submaximally symmetric models. Summarizing, weget a stronger form of Beloshapka's conjecture on the symmetry dimension ofhypersurfaces in $\mathbb{C}^4$.

On 3-nondegenerate CR manifolds in dimension 7 (II): the intransitive case