# Extensions 1→N→G→Q→1 with N=C3×C6 and Q=C3⋊C8

Direct product G=N×Q with N=C3×C6 and Q=C3⋊C8
dρLabelID
C3×C6×C3⋊C8144C3xC6xC3:C8432,469

Semidirect products G=N:Q with N=C3×C6 and Q=C3⋊C8
extensionφ:Q→Aut NdρLabelID
(C3×C6)⋊(C3⋊C8) = C2×C3⋊F9φ: C3⋊C8/C3C8 ⊆ Aut C3×C6488(C3xC6):(C3:C8)432,752
(C3×C6)⋊2(C3⋊C8) = C2×He33C8φ: C3⋊C8/C4S3 ⊆ Aut C3×C6144(C3xC6):2(C3:C8)432,136
(C3×C6)⋊3(C3⋊C8) = C2×He34C8φ: C3⋊C8/C4S3 ⊆ Aut C3×C6144(C3xC6):3(C3:C8)432,184
(C3×C6)⋊4(C3⋊C8) = C2×C334C8φ: C3⋊C8/C6C4 ⊆ Aut C3×C648(C3xC6):4(C3:C8)432,639
(C3×C6)⋊5(C3⋊C8) = C6×C324C8φ: C3⋊C8/C12C2 ⊆ Aut C3×C6144(C3xC6):5(C3:C8)432,485
(C3×C6)⋊6(C3⋊C8) = C2×C337C8φ: C3⋊C8/C12C2 ⊆ Aut C3×C6432(C3xC6):6(C3:C8)432,501

Non-split extensions G=N.Q with N=C3×C6 and Q=C3⋊C8
extensionφ:Q→Aut NdρLabelID
(C3×C6).(C3⋊C8) = C6.F9φ: C3⋊C8/C3C8 ⊆ Aut C3×C6488(C3xC6).(C3:C8)432,566
(C3×C6).2(C3⋊C8) = He33C16φ: C3⋊C8/C4S3 ⊆ Aut C3×C61446(C3xC6).2(C3:C8)432,30
(C3×C6).3(C3⋊C8) = C9⋊C48φ: C3⋊C8/C4S3 ⊆ Aut C3×C61446(C3xC6).3(C3:C8)432,31
(C3×C6).4(C3⋊C8) = He34C16φ: C3⋊C8/C4S3 ⊆ Aut C3×C61443(C3xC6).4(C3:C8)432,33
(C3×C6).5(C3⋊C8) = C2×C9⋊C24φ: C3⋊C8/C4S3 ⊆ Aut C3×C6144(C3xC6).5(C3:C8)432,142
(C3×C6).6(C3⋊C8) = C334C16φ: C3⋊C8/C6C4 ⊆ Aut C3×C6484(C3xC6).6(C3:C8)432,413
(C3×C6).7(C3⋊C8) = C3×C9⋊C16φ: C3⋊C8/C12C2 ⊆ Aut C3×C61442(C3xC6).7(C3:C8)432,28
(C3×C6).8(C3⋊C8) = C72.S3φ: C3⋊C8/C12C2 ⊆ Aut C3×C6432(C3xC6).8(C3:C8)432,32
(C3×C6).9(C3⋊C8) = C6×C9⋊C8φ: C3⋊C8/C12C2 ⊆ Aut C3×C6144(C3xC6).9(C3:C8)432,124
(C3×C6).10(C3⋊C8) = C2×C36.S3φ: C3⋊C8/C12C2 ⊆ Aut C3×C6432(C3xC6).10(C3:C8)432,178
(C3×C6).11(C3⋊C8) = C3×C24.S3φ: C3⋊C8/C12C2 ⊆ Aut C3×C6144(C3xC6).11(C3:C8)432,230
(C3×C6).12(C3⋊C8) = C337C16φ: C3⋊C8/C12C2 ⊆ Aut C3×C6432(C3xC6).12(C3:C8)432,231
(C3×C6).13(C3⋊C8) = C32×C3⋊C16central extension (φ=1)144(C3xC6).13(C3:C8)432,229

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