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Let  be the set of all 3 X 3 non-singular matrices  ( a b c d e f g h i ) , where a, b, c, d, e, f, g, h, i are integers modulo p. Then    is a group under matrix multiplication modulo p, of order ( p n − 1) ( p n - p ) ( p n - p 2 ) … … ( p n - p n −1). Let G be the subgroup of    defined by  G = { ( a b c d e f g h i ) ∈ G : | a b c d e f g h i | = 1 } . Then G is of order  ( p n − 1 ) ( p n − p ) ( p n − p 2 ) … … ( p n − p n − 1 ) p − 1 . Let L(G) be the lattice formed by all subgroups G. In this paper, we give the structure of the subgroups of order 21of L(G) in the case when P=2.

The Lattice Structure of the Subgroups of order 21 in the subgroup lattices of 3 X 3 Matrices over Z2