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Extensions 1→N→G→Q→1 with N=C3×C18 and Q=S3

Direct product G=N×Q with N=C3×C18 and Q=S3
dρLabelID
S3×C3×C18108S3xC3xC18324,137

Semidirect products G=N:Q with N=C3×C18 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C3×C18)⋊1S3 = C2×C32⋊C18φ: S3/C1 → S3 ⊆ Aut C3×C18366(C3xC18):1S3324,62
(C3×C18)⋊2S3 = C2×He3.C6φ: S3/C1 → S3 ⊆ Aut C3×C18543(C3xC18):2S3324,70
(C3×C18)⋊3S3 = C2×He3.2C6φ: S3/C1 → S3 ⊆ Aut C3×C18543(C3xC18):3S3324,72
(C3×C18)⋊4S3 = C2×C32⋊2D9φ: S3/C1 → S3 ⊆ Aut C3×C18366(C3xC18):4S3324,75
(C3×C18)⋊5S3 = C2×He3.3S3φ: S3/C1 → S3 ⊆ Aut C3×C18546+(C3xC18):5S3324,78
(C3×C18)⋊6S3 = C2×He3⋊S3φ: S3/C1 → S3 ⊆ Aut C3×C18546+(C3xC18):6S3324,79
(C3×C18)⋊7S3 = C2×He3.4S3φ: S3/C1 → S3 ⊆ Aut C3×C18546+(C3xC18):7S3324,147
(C3×C18)⋊8S3 = C2×He3.4C6φ: S3/C1 → S3 ⊆ Aut C3×C18543(C3xC18):8S3324,148
(C3×C18)⋊9S3 = C18×C3⋊S3φ: S3/C3 → C2 ⊆ Aut C3×C18108(C3xC18):9S3324,143
(C3×C18)⋊10S3 = C6×C9⋊S3φ: S3/C3 → C2 ⊆ Aut C3×C18108(C3xC18):10S3324,142
(C3×C18)⋊11S3 = C2×C32⋊4D9φ: S3/C3 → C2 ⊆ Aut C3×C18162(C3xC18):11S3324,149

Non-split extensions G=N.Q with N=C3×C18 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C3×C18).1S3 = C32⋊C36φ: S3/C1 → S3 ⊆ Aut C3×C18366(C3xC18).1S3324,7
(C3×C18).2S3 = C9⋊C36φ: S3/C1 → S3 ⊆ Aut C3×C18366(C3xC18).2S3324,9
(C3×C18).3S3 = He3.C12φ: S3/C1 → S3 ⊆ Aut C3×C181083(C3xC18).3S3324,15
(C3×C18).4S3 = He3.2C12φ: S3/C1 → S3 ⊆ Aut C3×C181083(C3xC18).4S3324,17
(C3×C18).5S3 = C2×C9⋊C18φ: S3/C1 → S3 ⊆ Aut C3×C18366(C3xC18).5S3324,64
(C3×C18).6S3 = C32⋊2Dic9φ: S3/C1 → S3 ⊆ Aut C3×C18366(C3xC18).6S3324,20
(C3×C18).7S3 = He3.3Dic3φ: S3/C1 → S3 ⊆ Aut C3×C181086-(C3xC18).7S3324,23
(C3×C18).8S3 = He3⋊Dic3φ: S3/C1 → S3 ⊆ Aut C3×C181086-(C3xC18).8S3324,24
(C3×C18).9S3 = 3- 1+2.Dic3φ: S3/C1 → S3 ⊆ Aut C3×C181086-(C3xC18).9S3324,25
(C3×C18).10S3 = C2×3- 1+2.S3φ: S3/C1 → S3 ⊆ Aut C3×C18546+(C3xC18).10S3324,80
(C3×C18).11S3 = C27⋊C12φ: S3/C1 → S3 ⊆ Aut C3×C181086-(C3xC18).11S3324,12
(C3×C18).12S3 = C2×C27⋊C6φ: S3/C1 → S3 ⊆ Aut C3×C18546+(C3xC18).12S3324,67
(C3×C18).13S3 = He3.4Dic3φ: S3/C1 → S3 ⊆ Aut C3×C181086-(C3xC18).13S3324,101
(C3×C18).14S3 = He3.5C12φ: S3/C1 → S3 ⊆ Aut C3×C181083(C3xC18).14S3324,102
(C3×C18).15S3 = C9×Dic9φ: S3/C3 → C2 ⊆ Aut C3×C18362(C3xC18).15S3324,6
(C3×C18).16S3 = D9×C18φ: S3/C3 → C2 ⊆ Aut C3×C18362(C3xC18).16S3324,61
(C3×C18).17S3 = C9×C3⋊Dic3φ: S3/C3 → C2 ⊆ Aut C3×C18108(C3xC18).17S3324,97
(C3×C18).18S3 = C3×Dic27φ: S3/C3 → C2 ⊆ Aut C3×C181082(C3xC18).18S3324,10
(C3×C18).19S3 = C9⋊Dic9φ: S3/C3 → C2 ⊆ Aut C3×C18324(C3xC18).19S3324,19
(C3×C18).20S3 = C27⋊Dic3φ: S3/C3 → C2 ⊆ Aut C3×C18324(C3xC18).20S3324,21
(C3×C18).21S3 = C6×D27φ: S3/C3 → C2 ⊆ Aut C3×C181082(C3xC18).21S3324,65
(C3×C18).22S3 = C2×C9⋊D9φ: S3/C3 → C2 ⊆ Aut C3×C18162(C3xC18).22S3324,74
(C3×C18).23S3 = C2×C27⋊S3φ: S3/C3 → C2 ⊆ Aut C3×C18162(C3xC18).23S3324,76
(C3×C18).24S3 = C3×C9⋊Dic3φ: S3/C3 → C2 ⊆ Aut C3×C18108(C3xC18).24S3324,96
(C3×C18).25S3 = C32⋊5Dic9φ: S3/C3 → C2 ⊆ Aut C3×C18324(C3xC18).25S3324,103
(C3×C18).26S3 = Dic3×C3×C9central extension (φ=1)108(C3xC18).26S3324,91

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