Extensions 1→N→G→Q→1 with N=D₄⋊C₄ and Q=D₇

Direct product G=N×Q with N=D₄⋊C₄ and Q=D₇

		d	ρ	Label	ID
D₇×D₄⋊C₄		112		D7xD4:C4	448,303

Semidirect products G=N:Q with N=D₄⋊C₄ and Q=D₇

extension	φ:Q→Out N	d	Label	ID
D₄⋊C₄⋊₁D₇ = Dic₇.SD₁₆	φ: D₇/C₇ → C₂ ⊆ Out D₄⋊C₄	224	D4:C4:1D7	448,294
D₄⋊C₄⋊₂D₇ = D₁₄⋊D₈	φ: D₇/C₇ → C₂ ⊆ Out D₄⋊C₄	224	D4:C4:2D7	448,309
D₄⋊C₄⋊₃D₇ = D₁₄⋊SD₁₆	φ: D₇/C₇ → C₂ ⊆ Out D₄⋊C₄	224	D4:C4:3D7	448,312
D₄⋊C₄⋊₄D₇ = D₄⋊D₂₈	φ: D₇/C₇ → C₂ ⊆ Out D₄⋊C₄	112	D4:C4:4D7	448,307
D₄⋊C₄⋊₅D₇ = D₁₄.D₈	φ: D₇/C₇ → C₂ ⊆ Out D₄⋊C₄	224	D4:C4:5D7	448,308
D₄⋊C₄⋊₆D₇ = D₄.D₂₈	φ: D₇/C₇ → C₂ ⊆ Out D₄⋊C₄	224	D4:C4:6D7	448,317
D₄⋊C₄⋊₇D₇ = C₅₆⋊₁C₄⋊C₂	φ: D₇/C₇ → C₂ ⊆ Out D₄⋊C₄	224	D4:C4:7D7	448,318
D₄⋊C₄⋊₈D₇ = D₂₈⋊₃D₄	φ: D₇/C₇ → C₂ ⊆ Out D₄⋊C₄	224	D4:C4:8D7	448,320
D₄⋊C₄⋊₉D₇ = Dic₁₄⋊₂D₄	φ: D₇/C₇ → C₂ ⊆ Out D₄⋊C₄	224	D4:C4:9D7	448,296
D₄⋊C₄⋊₁₀D₇ = D₄.₆D₂₈	φ: D₇/C₇ → C₂ ⊆ Out D₄⋊C₄	112	D4:C4:10D7	448,310
D₄⋊C₄⋊₁₁D₇ = D₁₄.SD₁₆	φ: D₇/C₇ → C₂ ⊆ Out D₄⋊C₄	224	D4:C4:11D7	448,311
D₄⋊C₄⋊₁₂D₇ = C₈⋊Dic₇⋊C₂	φ: D₇/C₇ → C₂ ⊆ Out D₄⋊C₄	224	D4:C4:12D7	448,313
D₄⋊C₄⋊₁₃D₇ = D₄⋊₃D₂₈	φ: D₇/C₇ → C₂ ⊆ Out D₄⋊C₄	224	D4:C4:13D7	448,315
D₄⋊C₄⋊₁₄D₇ = D₂₈.D₄	φ: D₇/C₇ → C₂ ⊆ Out D₄⋊C₄	224	D4:C4:14D7	448,321
D₄⋊C₄⋊₁₅D₇ = C₄⋊C₄.D₁₄	φ: D₇/C₇ → C₂ ⊆ Out D₄⋊C₄	224	D4:C4:15D7	448,298
D₄⋊C₄⋊₁₆D₇ = (D₄×D₇)⋊C₄	φ: D₇/C₇ → C₂ ⊆ Out D₄⋊C₄	112	D4:C4:16D7	448,304
D₄⋊C₄⋊₁₇D₇ = D₄⋊(C₄×D₇)	φ: D₇/C₇ → C₂ ⊆ Out D₄⋊C₄	224	D4:C4:17D7	448,305
D₄⋊C₄⋊₁₈D₇ = C₇⋊C₈⋊₁D₄	φ: D₇/C₇ → C₂ ⊆ Out D₄⋊C₄	224	D4:C4:18D7	448,314
D₄⋊C₄⋊₁₉D₇ = C₇⋊C₈⋊D₄	φ: D₇/C₇ → C₂ ⊆ Out D₄⋊C₄	224	D4:C4:19D7	448,316
D₄⋊C₄⋊₂₀D₇ = D₄⋊D₇⋊C₄	φ: D₇/C₇ → C₂ ⊆ Out D₄⋊C₄	224	D4:C4:20D7	448,319
D₄⋊C₄⋊₂₁D₇ = Dic₇⋊₄D₈	φ: trivial image	224	D4:C4:21D7	448,290
D₄⋊C₄⋊₂₂D₇ = D₄⋊₂D₇⋊C₄	φ: trivial image	224	D4:C4:22D7	448,306

Non-split extensions G=N.Q with N=D₄⋊C₄ and Q=D₇

extension	φ:Q→Out N	d	Label	ID
D₄⋊C₄.₁D₇ = (C₈×Dic₇)⋊C₂	φ: D₇/C₇ → C₂ ⊆ Out D₄⋊C₄	224	D4:C4.1D7	448,302
D₄⋊C₄.₂D₇ = Dic₇.D₈	φ: D₇/C₇ → C₂ ⊆ Out D₄⋊C₄	224	D4:C4.2D7	448,293
D₄⋊C₄.₃D₇ = D₄.₂Dic₁₄	φ: D₇/C₇ → C₂ ⊆ Out D₄⋊C₄	224	D4:C4.3D7	448,300
D₄⋊C₄.₄D₇ = Dic₁₄.D₄	φ: D₇/C₇ → C₂ ⊆ Out D₄⋊C₄	224	D4:C4.4D7	448,301
D₄⋊C₄.₅D₇ = D₄⋊Dic₁₄	φ: D₇/C₇ → C₂ ⊆ Out D₄⋊C₄	224	D4:C4.5D7	448,295
D₄⋊C₄.₆D₇ = D₄.Dic₁₄	φ: D₇/C₇ → C₂ ⊆ Out D₄⋊C₄	224	D4:C4.6D7	448,297
D₄⋊C₄.₇D₇ = D₄.D₇⋊C₄	φ: D₇/C₇ → C₂ ⊆ Out D₄⋊C₄	224	D4:C4.7D7	448,291
D₄⋊C₄.₈D₇ = C₂₈⋊Q₈⋊C₂	φ: D₇/C₇ → C₂ ⊆ Out D₄⋊C₄	224	D4:C4.8D7	448,299
D₄⋊C₄.₉D₇ = Dic₇⋊₆SD₁₆	φ: trivial image	224	D4:C4.9D7	448,292

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Extensions 1→N→G→Q→1 with N=D4⋊C4 and Q=D7

Extensions 1→N→G→Q→1 with N=D₄⋊C₄ and Q=D₇