Homogeneous strictly pseudoconvex hypersurfaces in $\mathbb C^3$ with two-dimensional isotropy groups

Strictly pseudoconvex non-spherical hypersurfaces in 3-dimensional complex space that are homogeneous with respect to local Lie groups of holomorphic transformations are studied. The author proved earlier that a Lie group $\operatorname{Aut}M$ acting transitively on such a manifold $M$ has dimension at most 7.
A complete list of homogeneous surfaces such that $\operatorname{Aut}M$ has dimension precisely 7 (and the corresponding isotropy subgroup has dimension precisely 2) is given. The main tools used in the paper are local normal equations describing the manifolds under consideration.