  In this article, we describe some maximal $3$-local subgroups of the Monster
simple group using vertex operator algebras (VOA). We first study the
holomorphic vertex operator algebra obtained by applying the orbifold
construction to the Leech lattice vertex operator algebra and a lift of a
fixed-point free isometry of order $3$ of the Leech lattice. We also consider
some of its special subVOAs and study their stabilizer subgroups using the
symmetries of the subVOAs. It turns out that these stabilizer subgroups are
$3$-local subgroups of its full automorphism group. As one of our main results,
we show that its full automorphism group is isomorphic to the Monster simple
group by using a $3$-local characterization and that the holomorphic VOA is
isomorphic to the Moonshine VOA. This approach allows us to obtain relatively
explicit descriptions of two maximal $3$-local subgroups of the shape
$3^{1+12}.2.\Suz{:}2$ and $3^8.\Omega^-(8,3).2$ in the Monster simple group.
