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We study supersolid-like crystalline structures emerging in the stationary states of a quasi-two-dimensional spin-orbit (SO)-coupled spin-2 condensate in the ferromagnetic, cyclic, and antiferro-magnetic phases by solving a mean-field model.Interplay of different strengths of SO coupling and interatomic interactions gives rise to a variety of non-trivial density patterns in the emergent solutions. For small SO-coupling strengths $γ$ ($γ\approx 0.5$), the ground state is an axisymmetric multi-ring soliton for polar, cyclic and weakly-ferromagnetic interactions, whereas for stronger-ferromagnetic interactions a circularly-asymmetric soliton emerges as the ground state.Depending on the values of interaction parameters, with an increase in SO-coupling strength, a stripe phase may also emerge as the ground state for polar and cyclic interactions. For intermediate values of SO-coupling strength ($γ\approx 1$), in addition to these solitons, one could have a quasi-degenerate triangular-lattice soliton in all magnetic phases. On further increasing the SO-coupling strength ($γ\gtrapprox 4$), a square-lattice and a superstripe soliton emerge as quasi-degenerate states. The emergence of all these solitons can be inferred from a study of solutions of the single-particle Hamiltonian.