  The phase topology of the integrable Hamiltonian system on $e(3)$ found by
V.V.Sokolov (2001) and generalizing the Kowalevski case is investigated. The
generalization contains, along with a homogeneous potential force field,
gyroscopic forces depending on the configurational variables. Relative
equilibria are classified, their type is calculated and the character of
stability is defined. The Smale diagrams of the case are found and the
classification of iso-energy manifolds of the reduced systems with two degrees
of freedom is given. The set of critical points of the complete momentum map is
represented as a union of critical subsystems; each critical subsystem is a
one-parameter family of almost Hamiltonian systems with one degree of freedom.
For all critical points we explicitly calculate the characteristic values
defining their type. We obtain the equations of the surfaces bearing the
bifurcation diagram of the momentum map. We give examples of the existing
iso-energy diagrams with a complete description of the corresponding rough
topology (of the regular Liouville tori and their bifurcations).
