  The enhanced power graph of a group $G$ is a simple undirected graph with
vertex set $G$ and two vertices are adjacent if they belong to same cyclic
subgroup. In this paper, we study distant properties and detour distant
properties such as closure, interior, distance degree sequence and eccentric
subgraph of the enhanced power graph of semidihedral group. Consequently, we
obtained the metric dimension and resolving polynomial of the enhanced power
graph of semidihedral group. At the final part of this paper, we obtained the
Laplacian spectrum of the enhanced power graph of semidihedral, dihedral and
generalized quaternion groups.
