  We studied the square-octagonal lattice of the transition metal
dichalcogenide MX$_2$ (with $M$=Mo, W; $X$=S, Se and Te), as an isomer of the
normal hexagonal compound of MX$_2$. By band structure calculations, we observe
the graphene-like Dirac band structure in a rectangular lattice of MX$_2$ with
nonsymmorphic space group symmetry. Two bands with van Hove singularity points
cross each at the Fermi energy, leading to two Dirac cones that locates at
opposite momenta. Spin-orbit coupling can open a nontrivial gap at these Dirac
points and induce the quantum spin Hall (QSH) phase, the 2D topological
insulator. Here, square-octagonal MX$_2$ structures realize the interesting
graphene physics, such as Dirac bands and QSH effect, in the transition metal
dichalcogenides.
