We have studied spin--charge--orbital orderings in a Mn³⁺/Mn⁴⁺mixed valence state on a hollandite-type lattice using unrestricted Hartree--Fock calculation on a multi-band Mn 3d--O 2p lattice model. The calculations show that all the Mn³⁺--Mn⁴⁺, Mn³⁺--Mn³⁺, and Mn⁴⁺--Mn⁴⁺superexchange interactions are ferromagnetic and play important roles to stabilize the charge and orbital ordering patterns. The most stable charge and orbital ordering pattern is consistent with the 1\times 1\times 1 orthorhombic or monoclinic structure of K<inf>1.6</inf>Mn<inf>8</inf>O<inf>16</inf>.