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We study different ways of symmetry fractionalization in Z2 spin liquids on the triangular lattice. Our classification can be used to identify the symmetry fractionalization in the Z2 spin liquid reported in recent density-matrix-renormalization-group simulations for J1-J2 spin model on the triangular lattice. We find 64 types of symmetry enriched Z2 spin liquid states on triangular lattice. Besides 8 states constructed in Schwinger-boson parton wavefunctions, 12 more states can be realized in Abrikosov-fermion parton construction. Within a larger gauge group than SU (2), the rest 40 states are also found in a spin-3/2 system. Among 20 types of Abrikosov-fermion Gutzwillerprojected wavefunctions, No.B5 state is a promising candidate for the Z2 spin liquid for J1-J2 spin model on the triangular lattice. No.B5 lies close to Dirac spin liquid (DSL). However, variational Monte Carlo simulation find that DSL has a good variational energy and J1-J2 spin model cannot open a gap for spinons on top of DSL to stabilize No.B5 state.

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