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