  We study the possibility of switching the types of symmetry breaking
bifurcation (SBB) in the cylinder shell waveguide with helical double-well
potential along propagation direction. This model is described by the
one-dimensional nonlinear Schr\"{o}dinger (NLS) equation. The symmetry- and
antisymmetry-breakings can be caused by increasing the applied voltage onto the
waveguide in the self-focusing and -defocusing cases, respectively. In the
self-focusing case, the type of SBB can be switched from supercritical to
subcritical. While in the self-defocusing case, the type of SBB can not be
switched because only one type of SBB is found.
