# Extensions 1→N→G→Q→1 with N=2+ 1+4 and Q=C6

Direct product G=N×Q with N=2+ 1+4 and Q=C6
dρLabelID
C6×2+ 1+448C6xES+(2,2)192,1534

Semidirect products G=N:Q with N=2+ 1+4 and Q=C6
extensionφ:Q→Out NdρLabelID
2+ 1+41C6 = C2≀A4φ: C6/C1C6 ⊆ Out 2+ 1+484+ES+(2,2):1C6192,201
2+ 1+42C6 = SD16.A4φ: C6/C1C6 ⊆ Out 2+ 1+4324ES+(2,2):2C6192,1018
2+ 1+43C6 = C2×Q8.A4φ: C6/C2C3 ⊆ Out 2+ 1+448ES+(2,2):3C6192,1502
2+ 1+44C6 = 2- 1+43C6φ: C6/C2C3 ⊆ Out 2+ 1+4324ES+(2,2):4C6192,1504
2+ 1+45C6 = C2×C23⋊A4φ: C6/C2C3 ⊆ Out 2+ 1+416ES+(2,2):5C6192,1508
2+ 1+46C6 = C3×D44D4φ: C6/C3C2 ⊆ Out 2+ 1+4244ES+(2,2):6C6192,886
2+ 1+47C6 = C3×C2≀C22φ: C6/C3C2 ⊆ Out 2+ 1+4244ES+(2,2):7C6192,890
2+ 1+48C6 = C3×D4○D8φ: C6/C3C2 ⊆ Out 2+ 1+4484ES+(2,2):8C6192,1465
2+ 1+49C6 = C3×D4○SD16φ: C6/C3C2 ⊆ Out 2+ 1+4484ES+(2,2):9C6192,1466
2+ 1+410C6 = C3×C2.C25φ: trivial image484ES+(2,2):10C6192,1536

Non-split extensions G=N.Q with N=2+ 1+4 and Q=C6
extensionφ:Q→Out NdρLabelID
2+ 1+4.1C6 = 2+ 1+4.C6φ: C6/C1C6 ⊆ Out 2+ 1+4164ES+(2,2).1C6192,202
2+ 1+4.2C6 = Q16.A4φ: C6/C1C6 ⊆ Out 2+ 1+4484+ES+(2,2).2C6192,1017
2+ 1+4.3C6 = 2+ 1+4.3C6φ: C6/C2C3 ⊆ Out 2+ 1+4164ES+(2,2).3C6192,1509
2+ 1+4.4C6 = C3×D4.9D4φ: C6/C3C2 ⊆ Out 2+ 1+4484ES+(2,2).4C6192,888
2+ 1+4.5C6 = C3×C23.7D4φ: C6/C3C2 ⊆ Out 2+ 1+4484ES+(2,2).5C6192,891

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