Extensions 1→N→G→Q→1 with N=D4 and Q=S4

Direct product G=N×Q with N=D4 and Q=S4
dρLabelID
D4×S4126+D4xS4192,1472

Semidirect products G=N:Q with N=D4 and Q=S4
extensionφ:Q→Out NdρLabelID
D4⋊S4 = D4⋊S4φ: S4/A4C2 ⊆ Out D4246+D4:S4192,974
D42S4 = D42S4φ: trivial image246D4:2S4192,1473

Non-split extensions G=N.Q with N=D4 and Q=S4
extensionφ:Q→Out NdρLabelID
D4.1S4 = A4⋊SD16φ: S4/A4C2 ⊆ Out D4246D4.1S4192,973
D4.2S4 = D4.S4φ: S4/A4C2 ⊆ Out D4324-D4.2S4192,989
D4.3S4 = D4.3S4φ: S4/A4C2 ⊆ Out D4324D4.3S4192,990
D4.4S4 = D4.4S4φ: trivial image164D4.4S4192,1485
D4.5S4 = D4.5S4φ: trivial image324-D4.5S4192,1486

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