# Extensions 1→N→G→Q→1 with N=2+ 1+4 and Q=S3

Direct product G=N×Q with N=2+ 1+4 and Q=S3
dρLabelID
S3×2+ 1+4248+S3xES+(2,2)192,1524

Semidirect products G=N:Q with N=2+ 1+4 and Q=S3
extensionφ:Q→Out NdρLabelID
2+ 1+41S3 = Q8.5S4φ: S3/C1S3 ⊆ Out 2+ 1+4244+ES+(2,2):1S3192,988
2+ 1+42S3 = Q8.6S4φ: S3/C1S3 ⊆ Out 2+ 1+4324ES+(2,2):2S3192,1483
2+ 1+43S3 = Q8.7S4φ: S3/C1S3 ⊆ Out 2+ 1+4324+ES+(2,2):3S3192,1484
2+ 1+44S3 = C23⋊S4φ: S3/C1S3 ⊆ Out 2+ 1+484+ES+(2,2):4S3192,1493
2+ 1+45S3 = Q82S4φ: S3/C1S3 ⊆ Out 2+ 1+484+ES+(2,2):5S3192,1494
2+ 1+46S3 = 2+ 1+46S3φ: S3/C3C2 ⊆ Out 2+ 1+4248+ES+(2,2):6S3192,800
2+ 1+47S3 = 2+ 1+47S3φ: S3/C3C2 ⊆ Out 2+ 1+4248+ES+(2,2):7S3192,803
2+ 1+48S3 = D12.32C23φ: S3/C3C2 ⊆ Out 2+ 1+4488+ES+(2,2):8S3192,1394
2+ 1+49S3 = D12.33C23φ: S3/C3C2 ⊆ Out 2+ 1+4488-ES+(2,2):9S3192,1395
2+ 1+410S3 = D6.C24φ: trivial image488-ES+(2,2):10S3192,1525

Non-split extensions G=N.Q with N=2+ 1+4 and Q=S3
extensionφ:Q→Out NdρLabelID
2+ 1+4.1S3 = Q8.4S4φ: S3/C1S3 ⊆ Out 2+ 1+4484ES+(2,2).1S3192,987
2+ 1+4.2S3 = C23.S4φ: S3/C1S3 ⊆ Out 2+ 1+4164ES+(2,2).2S3192,1491
2+ 1+4.3S3 = Q8.S4φ: S3/C1S3 ⊆ Out 2+ 1+4164ES+(2,2).3S3192,1492
2+ 1+4.4S3 = 2+ 1+4.4S3φ: S3/C3C2 ⊆ Out 2+ 1+4488-ES+(2,2).4S3192,801
2+ 1+4.5S3 = 2+ 1+4.5S3φ: S3/C3C2 ⊆ Out 2+ 1+4488-ES+(2,2).5S3192,802

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