  We describe the automorphism groups of all holomorphic vertex operator
algebras of central charge $24$ with non-trivial weight one Lie algebras by
using their constructions as simple current extensions. We also confirm a
conjecture of G. H\"ohn on the numbers of holomorphic vertex operator algebras
of central charge $24$ obtained as inequivalent simple current extensions of
certain vertex operator algebras, which gives another proof of the uniqueness
of holomorphic vertex operator algebras of central charge $24$ with non-trivial
weight one Lie algebras.
