  In this article, we study isomorphisms between simple current extensions of a
simple VOA. For example, we classify the isomorphism classes of simple current
extensions of some VOAs. Moreover, we consider the same simple current
extension and describe the normalizer of the abelian automorphism group
associated with this extension. In particular, we regard the moonshine module
as simple current extensions of five subVOAs V_L^+ for 2-elementary totally
even lattices L, and describe corresponding five normalizers of elementary
abelian 2-group in the automorphism group of the moonshine module in terms of
V_L^+. By using this description, we show that three of them form a Monster
amalgam.
