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We study supersolid-like crystalline structures emerging in the stationarystates of a quasi-two-dimensional spin-orbit (SO)-coupled spin-2 condensate inthe ferromagnetic, cyclic, and antiferro-magnetic phases by solving amean-field model.Interplay of different strengths of SO coupling andinteratomic interactions gives rise to a variety of non-trivial densitypatterns in the emergent solutions. For small SO-coupling strengths $\gamma$($\gamma \approx 0.5$), the ground state is an axisymmetric multi-ring solitonfor polar, cyclic and weakly-ferromagnetic interactions, whereas forstronger-ferromagnetic interactions a circularly-asymmetric soliton emerges asthe ground state.Depending on the values of interaction parameters, with anincrease in SO-coupling strength, a stripe phase may also emerge as the groundstate for polar and cyclic interactions. For intermediate values of SO-couplingstrength ($\gamma \approx 1$), in addition to these solitons, one could have aquasi-degenerate triangular-lattice soliton in all magnetic phases. On furtherincreasing the SO-coupling strength ($\gamma \gtrapprox 4$), a square-latticeand a superstripe soliton emerge as quasi-degenerate states. The emergence ofall these solitons can be inferred from a study of solutions of thesingle-particle Hamiltonian.

Supersolid-like solitons in spin-orbit coupled spin-2 condensate