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In this article, we construct three new holomorphic vertex operator algebrasof central charge $24$ using the $\mathbb{Z}_2$-orbifold constructionassociated to inner automorphisms. Their weight one subspaces has the Liealgebra 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 holomorphicvertex 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.

Orbifold construction of holomorphic vertex operator algebras associated to inner automorphisms