As an example, consider the dihedral group G = D 3 = Sym(X), where X is an equilateral triangle. We may decorate this with an arrow on one edge, obtaining an asymmetric figure X. Letting τ ∈ G be the reflection of the arrowed edge, the composite figure X = X ∪ τ X has a bidirectional arrow on that edge, and its symmetry group is H = {1, τ}. This subgroup is not normal, since gX may have the bi-arrow on a different edge, giving a different reflection symmetry group.