Extensions 1→N→G→Q→1 with N=Q8 and Q=S4

Direct product G=N×Q with N=Q8 and Q=S4

Semidirect products G=N:Q with N=Q8 and Q=S4
extensionφ:Q→Out NdρLabelID
Q81S4 = Q8⋊S4φ: S4/C22S3 ⊆ Out Q8246Q8:1S4192,1490
Q82S4 = Q82S4φ: S4/C22S3 ⊆ Out Q884+Q8:2S4192,1494
Q83S4 = Q83S4φ: S4/A4C2 ⊆ Out Q8246Q8:3S4192,976
Q84S4 = Q84S4φ: trivial image246Q8:4S4192,1478

Non-split extensions G=N.Q with N=Q8 and Q=S4
extensionφ:Q→Out NdρLabelID
Q8.1S4 = Q8.1S4φ: S4/C22S3 ⊆ Out Q8486-Q8.1S4192,1489
Q8.2S4 = Q8.S4φ: S4/C22S3 ⊆ Out Q8164Q8.2S4192,1492
Q8.3S4 = A42Q16φ: S4/A4C2 ⊆ Out Q8486-Q8.3S4192,975
Q8.4S4 = Q8.4S4φ: S4/A4C2 ⊆ Out Q8484Q8.4S4192,987
Q8.5S4 = Q8.5S4φ: S4/A4C2 ⊆ Out Q8244+Q8.5S4192,988
Q8.6S4 = Q8.6S4φ: trivial image324Q8.6S4192,1483
Q8.7S4 = Q8.7S4φ: trivial image324+Q8.7S4192,1484