  In this article, we construct three new holomorphic vertex operator algebras
of central charge $24$ using the $\mathbb{Z}_2$-orbifold construction
associated to inner automorphisms. Their weight one subspaces has the Lie
algebra structures $D_{7,3}A_{3,1}G_{2,1}$, $E_{7,3}A_{5,1}$, and
$A_{8,3}A_{2,1}^2$. In addition, we discuss the constructions of holomorphic
vertex operator algebras with Lie algebras $A_{5,6}C_{2,3}A_{1,2}$ and
$D_{6,5}A_{1,1}^2$ from holomorphic vertex operator algebras with Lie algebras
$C_{5,3}G_{2,2}A_{1,1}$ and $A_{4,5}^2$, respectively.
