We suggest a possible origin of noncollinear magnetic textures in ferromagnets (FMs) with the D3h and Td point group symmetries. Proposed mechanism is different from the Dzyaloshinskii-Moriya interaction (DMI). The DMI often induces linear-in-gradient terms in Ginzburg-Landau micromagnetic energy of a magnet in the form of the so-called Livshitz-invariants (LIs) that explain noncollinear magnetic order. In the considered symmetry classes all LIs are forbidden despite broken inversion symmetry. At the same time noncollinear textures are observed experimentally e.g. in monolayer Fe3GeTe2 that is characterized by magnetic lattice with D3h symmetry. We suggest that the spiral magnetic order observed in this case is governed by indirect four-spin interactions that have not been previously considered. Such interactions appear in micromagnetic energy as terms that are of the fourth order in magnetization and contain the first spatial derivative. We analyze the stability of spiral, skyrmion and bimeron solutions and find signatures of the proposed four-spin interactions in magnon spectra.  An analogous consideration is applied to magnets with Td point group symmetry of magnetic lattice.