# Extensions 1→N→G→Q→1 with N=C12 and Q=C22

Direct product G=N×Q with N=C12 and Q=C22
dρLabelID
C22×C1248C2^2xC1248,44

Semidirect products G=N:Q with N=C12 and Q=C22
extensionφ:Q→Aut NdρLabelID
C12⋊C22 = S3×D4φ: C22/C1C22 ⊆ Aut C12124+C12:C2^248,38
C122C22 = C2×D12φ: C22/C2C2 ⊆ Aut C1224C12:2C2^248,36
C123C22 = S3×C2×C4φ: C22/C2C2 ⊆ Aut C1224C12:3C2^248,35
C124C22 = C6×D4φ: C22/C2C2 ⊆ Aut C1224C12:4C2^248,45

Non-split extensions G=N.Q with N=C12 and Q=C22
extensionφ:Q→Aut NdρLabelID
C12.1C22 = D4⋊S3φ: C22/C1C22 ⊆ Aut C12244+C12.1C2^248,15
C12.2C22 = D4.S3φ: C22/C1C22 ⊆ Aut C12244-C12.2C2^248,16
C12.3C22 = Q82S3φ: C22/C1C22 ⊆ Aut C12244+C12.3C2^248,17
C12.4C22 = C3⋊Q16φ: C22/C1C22 ⊆ Aut C12484-C12.4C2^248,18
C12.5C22 = D42S3φ: C22/C1C22 ⊆ Aut C12244-C12.5C2^248,39
C12.6C22 = S3×Q8φ: C22/C1C22 ⊆ Aut C12244-C12.6C2^248,40
C12.7C22 = Q83S3φ: C22/C1C22 ⊆ Aut C12244+C12.7C2^248,41
C12.8C22 = C24⋊C2φ: C22/C2C2 ⊆ Aut C12242C12.8C2^248,6
C12.9C22 = D24φ: C22/C2C2 ⊆ Aut C12242+C12.9C2^248,7
C12.10C22 = Dic12φ: C22/C2C2 ⊆ Aut C12482-C12.10C2^248,8
C12.11C22 = C2×Dic6φ: C22/C2C2 ⊆ Aut C1248C12.11C2^248,34
C12.12C22 = S3×C8φ: C22/C2C2 ⊆ Aut C12242C12.12C2^248,4
C12.13C22 = C8⋊S3φ: C22/C2C2 ⊆ Aut C12242C12.13C2^248,5
C12.14C22 = C2×C3⋊C8φ: C22/C2C2 ⊆ Aut C1248C12.14C2^248,9
C12.15C22 = C4.Dic3φ: C22/C2C2 ⊆ Aut C12242C12.15C2^248,10
C12.16C22 = C4○D12φ: C22/C2C2 ⊆ Aut C12242C12.16C2^248,37
C12.17C22 = C3×D8φ: C22/C2C2 ⊆ Aut C12242C12.17C2^248,25
C12.18C22 = C3×SD16φ: C22/C2C2 ⊆ Aut C12242C12.18C2^248,26
C12.19C22 = C3×Q16φ: C22/C2C2 ⊆ Aut C12482C12.19C2^248,27
C12.20C22 = C6×Q8φ: C22/C2C2 ⊆ Aut C1248C12.20C2^248,46
C12.21C22 = C3×C4○D4φ: C22/C2C2 ⊆ Aut C12242C12.21C2^248,47
C12.22C22 = C3×M4(2)central extension (φ=1)242C12.22C2^248,24

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