  We construct orbifolds of holomorphic lattice Vertex Operator Algebras for
non-Abelian finite automorphism groups $G$. To this end, we construct twisted
modules for automorphisms $g$ together with the projective representation of
the centralizer of $g$ on the twisted module. This allows us to extract the
irreducible modules of the fixed point VOA $V^G$, and to compute their
characters and modular transformation properties. We then construct holomorphic
VOAs by adjoining such modules to $V^G$. Applying these methods to extremal
lattices in $d=48$ and $d=72$, we construct more than fifty new holomorphic
VOAs of central charge 48 and 72, many of which have a very small number of
light states.
