# Extensions 1→N→G→Q→1 with N=C3×C27 and Q=S3

Direct product G=N×Q with N=C3×C27 and Q=S3
dρLabelID
S3×C3×C27162S3xC3xC27486,112

Semidirect products G=N:Q with N=C3×C27 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C3×C27)⋊1S3 = C32⋊C54φ: S3/C1S3 ⊆ Aut C3×C27546(C3xC27):1S3486,16
(C3×C27)⋊2S3 = He3.C18φ: S3/C1S3 ⊆ Aut C3×C27813(C3xC27):2S3486,26
(C3×C27)⋊3S3 = He3.2C18φ: S3/C1S3 ⊆ Aut C3×C27813(C3xC27):3S3486,28
(C3×C27)⋊4S3 = C322D27φ: S3/C1S3 ⊆ Aut C3×C27546(C3xC27):4S3486,51
(C3×C27)⋊5S3 = He3.3D9φ: S3/C1S3 ⊆ Aut C3×C27816+(C3xC27):5S3486,58
(C3×C27)⋊6S3 = He3.4D9φ: S3/C1S3 ⊆ Aut C3×C27816+(C3xC27):6S3486,59
(C3×C27)⋊7S3 = He3.5D9φ: S3/C1S3 ⊆ Aut C3×C27816+(C3xC27):7S3486,163
(C3×C27)⋊8S3 = He3.5C18φ: S3/C1S3 ⊆ Aut C3×C27813(C3xC27):8S3486,164
(C3×C27)⋊9S3 = C3⋊S3×C27φ: S3/C3C2 ⊆ Aut C3×C27162(C3xC27):9S3486,161
(C3×C27)⋊10S3 = C3×C27⋊S3φ: S3/C3C2 ⊆ Aut C3×C27162(C3xC27):10S3486,160
(C3×C27)⋊11S3 = C324D27φ: S3/C3C2 ⊆ Aut C3×C27243(C3xC27):11S3486,184

Non-split extensions G=N.Q with N=C3×C27 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C3×C27).1S3 = C9⋊C54φ: S3/C1S3 ⊆ Aut C3×C27546(C3xC27).1S3486,30
(C3×C27).2S3 = C81⋊C6φ: S3/C1S3 ⊆ Aut C3×C27816+(C3xC27).2S3486,34
(C3×C27).3S3 = D9×C27φ: S3/C3C2 ⊆ Aut C3×C27542(C3xC27).3S3486,14
(C3×C27).4S3 = C3×D81φ: S3/C3C2 ⊆ Aut C3×C271622(C3xC27).4S3486,32
(C3×C27).5S3 = C9⋊D27φ: S3/C3C2 ⊆ Aut C3×C27243(C3xC27).5S3486,50
(C3×C27).6S3 = C81⋊S3φ: S3/C3C2 ⊆ Aut C3×C27243(C3xC27).6S3486,60

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