  We investigate quantum order by disorder in a frustrated spin nanotube formed
by wrapping a $J_1$-$J_2$ Heisenberg model at 45$^\circ$ around a cylinder.
Using Schwinger boson theory and Density Matrix Renormalization Group (DMRG),
we have computed the ground-state phase diagram to reveal a $\mathbb{Z}_2$
phase in which collinear spin stripes form a right or left handed helix around
the nanotube. We have derived an analytic estimate for the critical
$\eta_c=J_1/2J_2$ of the $\mathbb{Z}_2$ helical phase transition, which is in
agreement with the DMRG results. By evaluating the entanglement spectrum and
nonlocal string order parameters we discuss the topology of the
$\mathbb{Z}_2$-helical phase.
