One of the concepts in mathematics that developing rapidly today is Graph Theory. The development of Graph Theory has been combined with Group Theory, that is by representing a group in a graph. The intersection graph from group , noted by , is a graph whose vertices are all non-trivial subgroups of group and two distinct vertices are adjacent in if and only if . In this research the intersection graph of a Dihedral group, we looking for the shapes and numerical invariants. The results obtained are if for , then has a subgraphs and subgraphs , the girth of the graph is 3, radius and diameter of the graph in a row is 2 and 3, and the chromatic number of the graph is
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