▁and ▁[ 3 , 2 , 6 ]. ▁ ▁And ▁[[ 3 ], 2 ,[ 3 ]], ▁order ▁ 1 4 4 , ▁and ▁is ▁is omorphic ▁to ▁[ 6 , 2 , 6 ]. ▁ ▁And ▁[[ [ 3 ], 2 ,[ 3 ]] ], ▁order ▁ 2 8 8 , ▁is omorphic ▁to ▁. ▁The ▁ 6 – 6 ▁du op r ism ▁has ▁this ▁symmetry , ▁as ▁ ▁or ▁. ▁ ▁I onic ▁dimin ished ▁sub groups ▁are ▁[ 3 + , 2 , 3 ], ▁[ 3 , 2 , 3 + ], ▁order ▁ 1 8 . ▁ ▁The ▁double ▁dimin ished ▁subgroup ▁is ▁[ 3 + , 2 , 3 + ], ▁order ▁ 9 . ▁ ▁Ext ended ▁as ▁[[ 3 + , 2 , 3 + ]], ▁order ▁ 1 8 . ▁ ▁A ▁high ▁index ▁subgroup ▁is ▁[ 3 , 2 ] ▁, ▁order ▁ 1 2 , ▁index ▁ 3 , ▁which ▁is ▁is omorphic ▁to ▁the ▁di hed ral ▁symmetry ▁in ▁three ▁dimensions ▁group , ▁[ 3 , 2 ], ▁D 3 h . ▁ ▁[ 3 , 2 ]+ , ▁order ▁ 6 ▁ ▁Square ▁du op r ism atic ▁group ▁– ▁[ 4 , 2 , 4 ], ▁, ▁order ▁ 6 4 . ▁ ▁The ▁ch iral ▁subgroup ▁is ▁[ 4 , 2 , 4 ]+ , ▁order ▁ 3 2 . ▁ ▁Ext ended ▁, ▁order ▁ 1 2 8 . ▁The ▁ 4 – 4 ▁du op