  The evolution of structure property along the fission path in the superheavy
nucleus $^{256}$Sg is predicted through the multi-dimensional
potential-energy(or Routhian)-surface calculations,in which the
phenomenological deformed Woods-Saxon potential is adopted. Calculated nuclear
deformations and fission barriers for $^{256}_{106}$Sg$_{150}$ and its
neighbors, e.g., $^{258,260}$Sg, $^{254}$Rf and $^{252}$No are presented and
compared with other theoretical results. A series of energy maps and curves are
provided and used to evaluate the corresponding shape-instability properties,
especially in the directions of triaxial $\gamma$ and different hexadecapole
deformations (e.g., $\alpha_{40}$, $\alpha_{42}$ and $\alpha_{44}$). It is
found that the triaxial deformation may help the nucleus bypass the first
fission-barrier of the axial case. After the first minimum in the nuclear
energy surface, the fission pathway of the nucleus can be affected by $\gamma$
and hexadecapole deformation degrees of freedom. In addition, microscopic
single-particle structure, pairing and Coriolis effects are briefly
investigated and discussed.

Nuclear Theory