The magnetic structure of Fe5O6 is studied using a combination of the group-theoretical analysis and DFT + U calculations of the electronic spectrum. The calculations are performed for the magnetic k = (0, 0, 0) vector. The magnetic ground state corresponds to the orthogonal ordering of two magnetic subsystems: the magnetic moments of Fe2+/Fe3+ ions located at the octahedral sites (slabs of octahedra) are directed along the c axis and are antiferromagnetically ordered, whereas the magnetic moments of Fe2+ ions in trigonal prisms forming one-dimensional chains are directed along the b axis and are antiferromagnetically coupled along the c axis. The formation of a nonzero antiferromagnetic component of magnetic moments in the slabs of octahedra directed along the b axis is caused by the effect of magnetic chains on the three-dimensional magnetic structure.