▁Dou bl ings : ▁[[ p + , 2 , p + ]], ▁( ), ▁[[ 2 p , 2 + , 2 p ]], ▁[[ 2 p + , 2 + , 2 p + ] ]. ▁ ▁[ p , 2 , ∞ ], ▁( ), ▁it ▁represents ▁a ▁line ▁groups ▁in ▁ 3 - space , ▁▁ ▁[ ∞ , 2 , ∞ ], ▁() ▁it ▁represents ▁the ▁E uclidean ▁plane ▁symmetry ▁with ▁two ▁sets ▁of ▁parallel ▁mirror s ▁and ▁a ▁rect angular ▁domain ▁( orb if old ▁* 2 2 2 2 ). ▁ ▁Sub groups ▁include : ▁[ p + , 2 , q ], ▁( ), ▁[ p , 2 , q + ], ▁( ), ▁[ p + , 2 , q + ], ▁( ). ▁ ▁And ▁for ▁even ▁values : ▁[ 2 p , 2 + , 2 q ], ▁( ), ▁[ 2 p , 2 + , 2 q + ], ▁( ), ▁[( p , 2 )+ , 2 q ], ▁( ), ▁[ 2 p ,( 2 , q )+ ], ▁( ), ▁[( p , 2 )+ , 2 q + ], ▁( ), ▁[ 2 p + ,( 2 , q )+ ], ▁( ), ▁[ 2 p + , 2 + , 2 q + ], ▁( ), ▁and ▁comm unt ator ▁subgroup , ▁index ▁ 1 6 , ▁[ 2 p + , 2 + , 2 q + ]+ , ▁( ). ▁ ▁Dig onal