  We study SU(4)-symmetric ultracold fermionic mixture in the cubic optical
lattice with the variable tunneling amplitude along one particular
crystallographic axis in the crossover region from the two- to
three-dimensional spatial geometry. To theoretically analyze emerging magnetic
phases and physical observables, we describe the system in the framework of the
Fermi-Hubbard model and apply dynamical mean-field theory. We show that in two
limiting cases of anisotropy there are two phases with different
antiferromagnetic orderings in the zero temperature limit and determine a
region of their coexistence. We also study the stability regions of different
magnetically-ordered states and density profiles of the gas in the harmonic
optical trap.
