Extensions 1→N→G→Q→1 with N=D12 and Q=C4

Direct product G=NxQ with N=D12 and Q=C4
dρLabelID
C4xD1248C4xD1296,80

Semidirect products G=N:Q with N=D12 and Q=C4
extensionφ:Q→Out NdρLabelID
D12:1C4 = C42:4S3φ: C4/C2C2 ⊆ Out D12242D12:1C496,12
D12:2C4 = C2.D24φ: C4/C2C2 ⊆ Out D1248D12:2C496,28
D12:3C4 = C6.D8φ: C4/C2C2 ⊆ Out D1248D12:3C496,16
D12:4C4 = D12:C4φ: C4/C2C2 ⊆ Out D12244D12:4C496,32
D12:5C4 = Dic3:5D4φ: C4/C2C2 ⊆ Out D1248D12:5C496,100

Non-split extensions G=N.Q with N=D12 and Q=C4
extensionφ:Q→Out NdρLabelID
D12.C4 = D12.C4φ: C4/C2C2 ⊆ Out D12484D12.C496,114
D12.2C4 = C8oD12φ: trivial image482D12.2C496,108

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