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We analyze breaking of symmetries that belong to the double point groupD2h(TD) (three mutually perpendicular symmetry axes of the second order,inversion, and time reversal). Subgroup structure of the D2h(TD) groupindicates that there can be as much as 28 physically different, broken-symmetrymean-field schemes --- starting with solutions obeying all the symmetries ofthe D2h(TD) group, through 26 generic schemes in which only a non-trivialsubgroup of D2h(TD) is conserved, down to solutions that break all of theD2h(TD) symmetries. Choices of single-particle bases and the correspondingstructures of single-particle hermitian operators are discussed for severalsubgroups of D2h(TD).Comment: 10 RevTeX pages, companion paper in nucl-th/991207

Point symmetries in the Hartree-Fock approach. II. Symmetry-breaking schemes