Extensions 1→N→G→Q→1 with N=D4 and Q=C44

Direct product G=NxQ with N=D4 and Q=C44
dρLabelID
D4xC44176D4xC44352,153

Semidirect products G=N:Q with N=D4 and Q=C44
extensionφ:Q→Out NdρLabelID
D4:1C44 = C11xD4:C4φ: C44/C22C2 ⊆ Out D4176D4:1C44352,51
D4:2C44 = C11xC4wrC2φ: C44/C22C2 ⊆ Out D4882D4:2C44352,53

Non-split extensions G=N.Q with N=D4 and Q=C44
extensionφ:Q→Out NdρLabelID
D4.C44 = C11xC8oD4φ: trivial image1762D4.C44352,166

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