Extensions 1→N→G→Q→1 with N=D₇×C₄² and Q=C₂

Direct product G=N×Q with N=D₇×C₄² and Q=C₂

		d	ρ	Label	ID
D₇×C₂×C₄²		224		D7xC2xC4^2	448,924

Semidirect products G=N:Q with N=D₇×C₄² and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(D₇×C₄²)⋊₁C₂ = D₇×C₄≀C₂	φ: C₂/C₁ → C₂ ⊆ Out D₇×C₄²	56	4	(D7xC4^2):1C2	448,354
(D₇×C₄²)⋊₂C₂ = C₄×D₄⋊₂D₇	φ: C₂/C₁ → C₂ ⊆ Out D₇×C₄²	224		(D7xC4^2):2C2	448,989
(D₇×C₄²)⋊₃C₂ = C₄×D₄×D₇	φ: C₂/C₁ → C₂ ⊆ Out D₇×C₄²	112		(D7xC4^2):3C2	448,997
(D₇×C₄²)⋊₄C₂ = C₄².₂₂₈D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₇×C₄²	224		(D7xC4^2):4C2	448,1001
(D₇×C₄²)⋊₅C₂ = C₄².₂₂₉D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₇×C₄²	224		(D7xC4^2):5C2	448,1010
(D₇×C₄²)⋊₆C₂ = C₄×Q₈⋊₂D₇	φ: C₂/C₁ → C₂ ⊆ Out D₇×C₄²	224		(D7xC4^2):6C2	448,1026
(D₇×C₄²)⋊₇C₂ = C₄².₁₃₁D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₇×C₄²	224		(D7xC4^2):7C2	448,1033
(D₇×C₄²)⋊₈C₂ = C₄².₂₃₃D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₇×C₄²	224		(D7xC4^2):8C2	448,1121
(D₇×C₄²)⋊₉C₂ = D₇×C₄.₄D₄	φ: C₂/C₁ → C₂ ⊆ Out D₇×C₄²	112		(D7xC4^2):9C2	448,1126
(D₇×C₄²)⋊₁₀C₂ = C₄².₂₃₄D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₇×C₄²	224		(D7xC4^2):10C2	448,1133
(D₇×C₄²)⋊₁₁C₂ = C₄².₂₃₇D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₇×C₄²	224		(D7xC4^2):11C2	448,1144
(D₇×C₄²)⋊₁₂C₂ = D₇×C₄⋊₁D₄	φ: C₂/C₁ → C₂ ⊆ Out D₇×C₄²	112		(D7xC4^2):12C2	448,1167
(D₇×C₄²)⋊₁₃C₂ = C₄².₂₃₈D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₇×C₄²	224		(D7xC4^2):13C2	448,1169
(D₇×C₄²)⋊₁₄C₂ = C₄².₂₄₀D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₇×C₄²	224		(D7xC4^2):14C2	448,1178
(D₇×C₄²)⋊₁₅C₂ = C₄×C₄○D₂₈	φ: C₂/C₁ → C₂ ⊆ Out D₇×C₄²	224		(D7xC4^2):15C2	448,927
(D₇×C₄²)⋊₁₆C₂ = D₇×C₄²⋊C₂	φ: C₂/C₁ → C₂ ⊆ Out D₇×C₄²	112		(D7xC4^2):16C2	448,973
(D₇×C₄²)⋊₁₇C₂ = C₄².₁₈₈D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₇×C₄²	224		(D7xC4^2):17C2	448,975
(D₇×C₄²)⋊₁₈C₂ = C₄².₉₃D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₇×C₄²	224		(D7xC4^2):18C2	448,981
(D₇×C₄²)⋊₁₉C₂ = D₇×C₄²⋊₂C₂	φ: C₂/C₁ → C₂ ⊆ Out D₇×C₄²	112		(D7xC4^2):19C2	448,1156
(D₇×C₄²)⋊₂₀C₂ = C₄².₁₈₉D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₇×C₄²	224		(D7xC4^2):20C2	448,1159

Non-split extensions G=N.Q with N=D₇×C₄² and Q=C₂

extension	φ:Q→Out N	d	Label	ID
(D₇×C₄²).₁C₂ = D₇×C₄⋊C₈	φ: C₂/C₁ → C₂ ⊆ Out D₇×C₄²	224	(D7xC4^2).1C2	448,366
(D₇×C₄²).₂C₂ = C₄².₂₀₀D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₇×C₄²	224	(D7xC4^2).2C2	448,367
(D₇×C₄²).₃C₂ = C₄².₂₀₂D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₇×C₄²	224	(D7xC4^2).3C2	448,369
(D₇×C₄²).₄C₂ = C₂₈⋊M₄(2)	φ: C₂/C₁ → C₂ ⊆ Out D₇×C₄²	224	(D7xC4^2).4C2	448,371
(D₇×C₄²).₅C₂ = C₄×Q₈×D₇	φ: C₂/C₁ → C₂ ⊆ Out D₇×C₄²	224	(D7xC4^2).5C2	448,1024
(D₇×C₄²).₆C₂ = C₄².₂₃₂D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₇×C₄²	224	(D7xC4^2).6C2	448,1031
(D₇×C₄²).₇C₂ = D₇×C₄².C₂	φ: C₂/C₁ → C₂ ⊆ Out D₇×C₄²	224	(D7xC4^2).7C2	448,1140
(D₇×C₄²).₈C₂ = C₄².₂₃₆D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₇×C₄²	224	(D7xC4^2).8C2	448,1141
(D₇×C₄²).₉C₂ = D₇×C₄⋊Q₈	φ: C₂/C₁ → C₂ ⊆ Out D₇×C₄²	224	(D7xC4^2).9C2	448,1176
(D₇×C₄²).₁₀C₂ = C₄².₂₄₁D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₇×C₄²	224	(D7xC4^2).10C2	448,1181
(D₇×C₄²).₁₁C₂ = C₄².₂₈₂D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₇×C₄²	224	(D7xC4^2).11C2	448,219
(D₇×C₄²).₁₂C₂ = C₄×C₈⋊D₇	φ: C₂/C₁ → C₂ ⊆ Out D₇×C₄²	224	(D7xC4^2).12C2	448,221
(D₇×C₄²).₁₃C₂ = D₇×C₈⋊C₄	φ: C₂/C₁ → C₂ ⊆ Out D₇×C₄²	224	(D7xC4^2).13C2	448,238
(D₇×C₄²).₁₄C₂ = C₄².₁₈₂D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₇×C₄²	224	(D7xC4^2).14C2	448,239
(D₇×C₄²).₁₅C₂ = Dic₇.C₄²	φ: C₂/C₁ → C₂ ⊆ Out D₇×C₄²	224	(D7xC4^2).15C2	448,241
(D₇×C₄²).₁₆C₂ = D₇×C₄×C₈	φ: trivial image	224	(D7xC4^2).16C2	448,218

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=D7×C42 and Q=C2

Extensions 1→N→G→Q→1 with N=D₇×C₄² and Q=C₂