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The change in the arrangement of magnetic dipole moments in a magnetic metasurface, due to the influence of an external static magnetic field, is discussed. Each meta-atom of the metasurface is composed of three identical disk-shaped resonators (trimer) made of magnetically saturated ferrite. To provide physical insight, full-wave numerical simulations of the near fields and transmission characteristics of the metasurface are complemented by the theoretical description based on the multipole decomposition method. With these methods, the study of eigenmodes and scattering conditions of a single magnetic resonator, trimer, and their array forming the metasurface is performed. It is found that the magnetic dipole-based collective hybrid mode of the trimer can be gradually transformed from the radial (pseudomonopole) to azimuthal (toroidal) order and vice versa by varying the bias magnetic field strength. This is because the magnetic dipole moment of each individual disk constituting the trimer undergoes rotation as the bias magnetic field strength changes. This transition between two orders is accompanied by various patterns of localization of the electric field inside the meta-atoms. Due to the unique field configuration of these modes, the proposed metasurface can be considered for designing magnetic field sensors and nonreciprocal devices.