2 + , 2 + ], ▁[ 2 + ,( 2 , 2 )+ ], ▁[( 2 , 2 )+ , 2 + ] ▁order ▁ 4 . ▁ ▁The ▁triple ▁dimin ished ▁subgroup ▁is ▁[ 2 + , 2 + , 2 + ], ▁( ), ▁order ▁ 2 . ▁It ▁is ▁a ▁ 2 - fold ▁double ▁rotation ▁and ▁a ▁ 4 D ▁central ▁in version . ▁ ▁Half ▁subgroup ▁is ▁[ 1 + , 2 , 2 , 2 ] =[ 1 , 2 , 2 ], ▁order ▁ 8 . ▁ ▁Tri angular ▁du op r ism atic ▁group ▁– ▁[ 3 , 2 , 3 ], ▁, ▁order ▁ 3 6 . ▁ ▁The ▁ch iral ▁subgroup ▁is ▁[ 3 , 2 , 3 ]+ , ▁order ▁ 1 8 . ▁ ▁Ext ended ▁, ▁order ▁ 7 2 . ▁The ▁ 3 - 3 ▁du op r ism ▁has ▁this ▁extended ▁symmetry , ▁. ▁ ▁The ▁ch iral ▁extended ▁group ▁is ▁+ , ▁order ▁ 3 6 . ▁ ▁Ext ended ▁ch iral ▁subgroup ▁is ▁[[ 3 , 2 , 3 ]+ ], ▁order ▁ 3 6 , ▁with ▁rot ore f lection ▁gener ators . ▁It ▁is ▁is omorphic ▁to ▁the ▁abstract ▁group ▁( 4 , 4 | 2 , 3 ). ▁ ▁Other ▁extended ▁[[ 3 ], 2 , 3 ], ▁[ 3 , 2 ,[ 3 ]], ▁order ▁ 7 2 , ▁and ▁are ▁is omorphic ▁to ▁[ 6 , 2 , 3 ]