Extensions 1→N→G→Q→1 with N=C₇×D₄ and Q=C₆

Direct product G=N×Q with N=C₇×D₄ and Q=C₆

		d	ρ	Label	ID
D₄×C₄₂		168		D4xC42	336,205

Semidirect products G=N:Q with N=C₇×D₄ and Q=C₆

extension	φ:Q→Out N	d	ρ	Label	ID
(C₇×D₄)⋊₁C₆ = D₄⋊F₇	φ: C₆/C₁ → C₆ ⊆ Out C₇×D₄	56	12+	(C7xD4):1C6	336,18
(C₇×D₄)⋊₂C₆ = D₄×F₇	φ: C₆/C₁ → C₆ ⊆ Out C₇×D₄	28	12+	(C7xD4):2C6	336,125
(C₇×D₄)⋊₃C₆ = D₄⋊₂F₇	φ: C₆/C₁ → C₆ ⊆ Out C₇×D₄	56	12-	(C7xD4):3C6	336,126
(C₇×D₄)⋊₄C₆ = D₈×C₇⋊C₃	φ: C₆/C₁ → C₆ ⊆ Out C₇×D₄	56	6	(C7xD4):4C6	336,53
(C₇×D₄)⋊₅C₆ = C₂×D₄×C₇⋊C₃	φ: C₆/C₂ → C₃ ⊆ Out C₇×D₄	56		(C7xD4):5C6	336,165
(C₇×D₄)⋊₆C₆ = C₄○D₄×C₇⋊C₃	φ: C₆/C₂ → C₃ ⊆ Out C₇×D₄	56	6	(C7xD4):6C6	336,167
(C₇×D₄)⋊₇C₆ = C₃×D₄⋊D₇	φ: C₆/C₃ → C₂ ⊆ Out C₇×D₄	168	4	(C7xD4):7C6	336,69
(C₇×D₄)⋊₈C₆ = C₃×D₄×D₇	φ: C₆/C₃ → C₂ ⊆ Out C₇×D₄	84	4	(C7xD4):8C6	336,178
(C₇×D₄)⋊₉C₆ = C₃×D₄⋊₂D₇	φ: C₆/C₃ → C₂ ⊆ Out C₇×D₄	168	4	(C7xD4):9C6	336,179
(C₇×D₄)⋊₁₀C₆ = D₈×C₂₁	φ: C₆/C₃ → C₂ ⊆ Out C₇×D₄	168	2	(C7xD4):10C6	336,111
(C₇×D₄)⋊₁₁C₆ = C₄○D₄×C₂₁	φ: trivial image	168	2	(C7xD4):11C6	336,207

Non-split extensions G=N.Q with N=C₇×D₄ and Q=C₆

extension	φ:Q→Out N	d	ρ	Label	ID
(C₇×D₄).₁C₆ = D₄.F₇	φ: C₆/C₁ → C₆ ⊆ Out C₇×D₄	56	12-	(C7xD4).1C6	336,19
(C₇×D₄).₂C₆ = SD₁₆×C₇⋊C₃	φ: C₆/C₁ → C₆ ⊆ Out C₇×D₄	56	6	(C7xD4).2C6	336,54
(C₇×D₄).₃C₆ = C₃×D₄.D₇	φ: C₆/C₃ → C₂ ⊆ Out C₇×D₄	168	4	(C7xD4).3C6	336,70
(C₇×D₄).₄C₆ = SD₁₆×C₂₁	φ: C₆/C₃ → C₂ ⊆ Out C₇×D₄	168	2	(C7xD4).4C6	336,112

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁