# Extensions 1→N→G→Q→1 with N=C3×Q8 and Q=C6

Direct product G=N×Q with N=C3×Q8 and Q=C6
dρLabelID
Q8×C3×C6144Q8xC3xC6144,180

Semidirect products G=N:Q with N=C3×Q8 and Q=C6
extensionφ:Q→Out NdρLabelID
(C3×Q8)⋊C6 = S3×SL2(𝔽3)φ: C6/C1C6 ⊆ Out C3×Q8244-(C3xQ8):C6144,128
(C3×Q8)⋊2C6 = C6×SL2(𝔽3)φ: C6/C2C3 ⊆ Out C3×Q848(C3xQ8):2C6144,156
(C3×Q8)⋊3C6 = C3×Q82S3φ: C6/C3C2 ⊆ Out C3×Q8484(C3xQ8):3C6144,82
(C3×Q8)⋊4C6 = C3×S3×Q8φ: C6/C3C2 ⊆ Out C3×Q8484(C3xQ8):4C6144,164
(C3×Q8)⋊5C6 = C3×Q83S3φ: C6/C3C2 ⊆ Out C3×Q8484(C3xQ8):5C6144,165
(C3×Q8)⋊6C6 = C32×SD16φ: C6/C3C2 ⊆ Out C3×Q872(C3xQ8):6C6144,107
(C3×Q8)⋊7C6 = C32×C4○D4φ: trivial image72(C3xQ8):7C6144,181

Non-split extensions G=N.Q with N=C3×Q8 and Q=C6
extensionφ:Q→Out NdρLabelID
(C3×Q8).C6 = Dic3.A4φ: C6/C1C6 ⊆ Out C3×Q8484+(C3xQ8).C6144,127
(C3×Q8).2C6 = C2×Q8⋊C9φ: C6/C2C3 ⊆ Out C3×Q8144(C3xQ8).2C6144,35
(C3×Q8).3C6 = Q8.C18φ: C6/C2C3 ⊆ Out C3×Q8722(C3xQ8).3C6144,36
(C3×Q8).4C6 = C3×C4.A4φ: C6/C2C3 ⊆ Out C3×Q8482(C3xQ8).4C6144,157
(C3×Q8).5C6 = C3×C3⋊Q16φ: C6/C3C2 ⊆ Out C3×Q8484(C3xQ8).5C6144,83
(C3×Q8).6C6 = C9×SD16φ: C6/C3C2 ⊆ Out C3×Q8722(C3xQ8).6C6144,26
(C3×Q8).7C6 = C9×Q16φ: C6/C3C2 ⊆ Out C3×Q81442(C3xQ8).7C6144,27
(C3×Q8).8C6 = C32×Q16φ: C6/C3C2 ⊆ Out C3×Q8144(C3xQ8).8C6144,108
(C3×Q8).9C6 = Q8×C18φ: trivial image144(C3xQ8).9C6144,49
(C3×Q8).10C6 = C9×C4○D4φ: trivial image722(C3xQ8).10C6144,50

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