Abstract: The decomposition of the normal semigroup lattices of Clifford semigroups is studied, and then confirms the necessary and sufficient conditions for normal subsemigroup lattices of Clifford semigroups to be distributive lattices (upper semidistributive lattices, lower semidistributive lattices).

Key words: Clifford semigroups, normal subsemigroup lattices, distributive lattices, upper semidistributive lattices, lower semidistributive lattices