Extensions 1→N→G→Q→1 with N=2+ 1+4 and Q=C2

Direct product G=N×Q with N=2+ 1+4 and Q=C2
dρLabelID
C2×2+ 1+416C2xES+(2,2)64,264

Semidirect products G=N:Q with N=2+ 1+4 and Q=C2
extensionφ:Q→Out NdρLabelID
2+ 1+41C2 = D44D4φ: C2/C1C2 ⊆ Out 2+ 1+484+ES+(2,2):1C264,134
2+ 1+42C2 = C2≀C22φ: C2/C1C2 ⊆ Out 2+ 1+484+ES+(2,2):2C264,138
2+ 1+43C2 = D4○D8φ: C2/C1C2 ⊆ Out 2+ 1+4164+ES+(2,2):3C264,257
2+ 1+44C2 = D4○SD16φ: C2/C1C2 ⊆ Out 2+ 1+4164ES+(2,2):4C264,258
2+ 1+45C2 = C2.C25φ: trivial image164ES+(2,2):5C264,266

Non-split extensions G=N.Q with N=2+ 1+4 and Q=C2
extensionφ:Q→Out NdρLabelID
2+ 1+4.1C2 = D4.9D4φ: C2/C1C2 ⊆ Out 2+ 1+4164ES+(2,2).1C264,136
2+ 1+4.2C2 = C23.7D4φ: C2/C1C2 ⊆ Out 2+ 1+4164ES+(2,2).2C264,139

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