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Extensions 1→N→G→Q→1 with N=C3×C24 and Q=S3

Direct product G=N×Q with N=C3×C24 and Q=S3
dρLabelID
S3×C3×C24144S3xC3xC24432,464

Semidirect products G=N:Q with N=C3×C24 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C3×C24)⋊1S3 = He3⋊4D8φ: S3/C1 → S3 ⊆ Aut C3×C24726+(C3xC24):1S3432,118
(C3×C24)⋊2S3 = He3⋊5D8φ: S3/C1 → S3 ⊆ Aut C3×C24726(C3xC24):2S3432,176
(C3×C24)⋊3S3 = He3⋊6SD16φ: S3/C1 → S3 ⊆ Aut C3×C24726(C3xC24):3S3432,117
(C3×C24)⋊4S3 = He3⋊7SD16φ: S3/C1 → S3 ⊆ Aut C3×C24726(C3xC24):4S3432,175
(C3×C24)⋊5S3 = C8×C32⋊C6φ: S3/C1 → S3 ⊆ Aut C3×C24726(C3xC24):5S3432,115
(C3×C24)⋊6S3 = C8×He3⋊C2φ: S3/C1 → S3 ⊆ Aut C3×C24723(C3xC24):6S3432,173
(C3×C24)⋊7S3 = He3⋊5M4(2)φ: S3/C1 → S3 ⊆ Aut C3×C24726(C3xC24):7S3432,116
(C3×C24)⋊8S3 = He3⋊6M4(2)φ: S3/C1 → S3 ⊆ Aut C3×C24726(C3xC24):8S3432,174
(C3×C24)⋊9S3 = C33⋊12D8φ: S3/C3 → C2 ⊆ Aut C3×C24216(C3xC24):9S3432,499
(C3×C24)⋊10S3 = C3×C32⋊5D8φ: S3/C3 → C2 ⊆ Aut C3×C24144(C3xC24):10S3432,483
(C3×C24)⋊11S3 = C33⋊21SD16φ: S3/C3 → C2 ⊆ Aut C3×C24216(C3xC24):11S3432,498
(C3×C24)⋊12S3 = C3×C24⋊2S3φ: S3/C3 → C2 ⊆ Aut C3×C24144(C3xC24):12S3432,482
(C3×C24)⋊13S3 = C32×D24φ: S3/C3 → C2 ⊆ Aut C3×C24144(C3xC24):13S3432,467
(C3×C24)⋊14S3 = C3⋊S3×C24φ: S3/C3 → C2 ⊆ Aut C3×C24144(C3xC24):14S3432,480
(C3×C24)⋊15S3 = C8×C33⋊C2φ: S3/C3 → C2 ⊆ Aut C3×C24216(C3xC24):15S3432,496
(C3×C24)⋊16S3 = C33⋊15M4(2)φ: S3/C3 → C2 ⊆ Aut C3×C24216(C3xC24):16S3432,497
(C3×C24)⋊17S3 = C3×C24⋊S3φ: S3/C3 → C2 ⊆ Aut C3×C24144(C3xC24):17S3432,481
(C3×C24)⋊18S3 = C32×C24⋊C2φ: S3/C3 → C2 ⊆ Aut C3×C24144(C3xC24):18S3432,466
(C3×C24)⋊19S3 = C32×C8⋊S3φ: S3/C3 → C2 ⊆ Aut C3×C24144(C3xC24):19S3432,465

Non-split extensions G=N.Q with N=C3×C24 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C3×C24).1S3 = He3⋊4Q16φ: S3/C1 → S3 ⊆ Aut C3×C241446-(C3xC24).1S3432,114
(C3×C24).2S3 = C72.C6φ: S3/C1 → S3 ⊆ Aut C3×C241446-(C3xC24).2S3432,119
(C3×C24).3S3 = D72⋊C3φ: S3/C1 → S3 ⊆ Aut C3×C24726+(C3xC24).3S3432,123
(C3×C24).4S3 = He3⋊5Q16φ: S3/C1 → S3 ⊆ Aut C3×C241446(C3xC24).4S3432,177
(C3×C24).5S3 = C72⋊2C6φ: S3/C1 → S3 ⊆ Aut C3×C24726(C3xC24).5S3432,122
(C3×C24).6S3 = He3⋊3C16φ: S3/C1 → S3 ⊆ Aut C3×C241446(C3xC24).6S3432,30
(C3×C24).7S3 = C9⋊C48φ: S3/C1 → S3 ⊆ Aut C3×C241446(C3xC24).7S3432,31
(C3×C24).8S3 = He3⋊4C16φ: S3/C1 → S3 ⊆ Aut C3×C241443(C3xC24).8S3432,33
(C3×C24).9S3 = C8×C9⋊C6φ: S3/C1 → S3 ⊆ Aut C3×C24726(C3xC24).9S3432,120
(C3×C24).10S3 = C72⋊C6φ: S3/C1 → S3 ⊆ Aut C3×C24726(C3xC24).10S3432,121
(C3×C24).11S3 = C24.D9φ: S3/C3 → C2 ⊆ Aut C3×C24432(C3xC24).11S3432,168
(C3×C24).12S3 = C72⋊1S3φ: S3/C3 → C2 ⊆ Aut C3×C24216(C3xC24).12S3432,172
(C3×C24).13S3 = C33⋊12Q16φ: S3/C3 → C2 ⊆ Aut C3×C24432(C3xC24).13S3432,500
(C3×C24).14S3 = C3×Dic36φ: S3/C3 → C2 ⊆ Aut C3×C241442(C3xC24).14S3432,104
(C3×C24).15S3 = C3×D72φ: S3/C3 → C2 ⊆ Aut C3×C241442(C3xC24).15S3432,108
(C3×C24).16S3 = C3×C32⋊5Q16φ: S3/C3 → C2 ⊆ Aut C3×C24144(C3xC24).16S3432,484
(C3×C24).17S3 = C24⋊D9φ: S3/C3 → C2 ⊆ Aut C3×C24216(C3xC24).17S3432,171
(C3×C24).18S3 = C3×C72⋊C2φ: S3/C3 → C2 ⊆ Aut C3×C241442(C3xC24).18S3432,107
(C3×C24).19S3 = C32×Dic12φ: S3/C3 → C2 ⊆ Aut C3×C24144(C3xC24).19S3432,468
(C3×C24).20S3 = C3×C9⋊C16φ: S3/C3 → C2 ⊆ Aut C3×C241442(C3xC24).20S3432,28
(C3×C24).21S3 = C72.S3φ: S3/C3 → C2 ⊆ Aut C3×C24432(C3xC24).21S3432,32
(C3×C24).22S3 = D9×C24φ: S3/C3 → C2 ⊆ Aut C3×C241442(C3xC24).22S3432,105
(C3×C24).23S3 = C8×C9⋊S3φ: S3/C3 → C2 ⊆ Aut C3×C24216(C3xC24).23S3432,169
(C3×C24).24S3 = C72⋊S3φ: S3/C3 → C2 ⊆ Aut C3×C24216(C3xC24).24S3432,170
(C3×C24).25S3 = C3×C24.S3φ: S3/C3 → C2 ⊆ Aut C3×C24144(C3xC24).25S3432,230
(C3×C24).26S3 = C33⋊7C16φ: S3/C3 → C2 ⊆ Aut C3×C24432(C3xC24).26S3432,231
(C3×C24).27S3 = C3×C8⋊D9φ: S3/C3 → C2 ⊆ Aut C3×C241442(C3xC24).27S3432,106
(C3×C24).28S3 = C32×C3⋊C16central extension (φ=1)144(C3xC24).28S3432,229

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