Extensions 1→N→G→Q→1 with N=D₄×Dic₇ and Q=C₂

Direct product G=N×Q with N=D₄×Dic₇ and Q=C₂

		d	ρ	Label	ID
C₂×D₄×Dic₇		224		C2xD4xDic7	448,1248

Semidirect products G=N:Q with N=D₄×Dic₇ and Q=C₂

extension	φ:Q→Out N	d	Label	ID
(D₄×Dic₇)⋊₁C₂ = Dic₇⋊₄D₈	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7):1C2	448,290
(D₄×Dic₇)⋊₂C₂ = D₄⋊D₇⋊C₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7):2C2	448,319
(D₄×Dic₇)⋊₃C₂ = D₈×Dic₇	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7):3C2	448,683
(D₄×Dic₇)⋊₄C₂ = Dic₇⋊D₈	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7):4C2	448,684
(D₄×Dic₇)⋊₅C₂ = D₈⋊Dic₇	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7):5C2	448,686
(D₄×Dic₇)⋊₆C₂ = (C₂×D₈).D₇	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7):6C2	448,687
(D₄×Dic₇)⋊₇C₂ = (C₇×D₄).D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7):7C2	448,699
(D₄×Dic₇)⋊₈C₂ = C₄²⋊₁₁D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	112	(D4xDic7):8C2	448,998
(D₄×Dic₇)⋊₉C₂ = C₄².₁₀₈D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7):9C2	448,999
(D₄×Dic₇)⋊₁₀C₂ = C₂⁴.₅₆D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	112	(D4xDic7):10C2	448,1039
(D₄×Dic₇)⋊₁₁C₂ = C₂⁴.₃₂D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	112	(D4xDic7):11C2	448,1040
(D₄×Dic₇)⋊₁₂C₂ = C₂⁴.₃₃D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	112	(D4xDic7):12C2	448,1044
(D₄×Dic₇)⋊₁₃C₂ = C₂⁴.₃₅D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	112	(D4xDic7):13C2	448,1046
(D₄×Dic₇)⋊₁₄C₂ = C₂₈⋊(C₄○D₄)	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7):14C2	448,1049
(D₄×Dic₇)⋊₁₅C₂ = Dic₁₄⋊₁₉D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7):15C2	448,1051
(D₄×Dic₇)⋊₁₆C₂ = C₄⋊C₄.₁₇₈D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7):16C2	448,1053
(D₄×Dic₇)⋊₁₇C₂ = C₁₄.₃₄2₊¹⁺⁴	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7):17C2	448,1054
(D₄×Dic₇)⋊₁₈C₂ = C₁₄.₃₅2₊¹⁺⁴	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7):18C2	448,1055
(D₄×Dic₇)⋊₁₉C₂ = C₁₄.₇₁2_-¹⁺⁴	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7):19C2	448,1056
(D₄×Dic₇)⋊₂₀C₂ = C₄⋊C₄⋊₂₁D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	112	(D4xDic7):20C2	448,1059
(D₄×Dic₇)⋊₂₁C₂ = C₁₄.₇₃2_-¹⁺⁴	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7):21C2	448,1064
(D₄×Dic₇)⋊₂₂C₂ = C₁₄.₄₃2₊¹⁺⁴	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7):22C2	448,1067
(D₄×Dic₇)⋊₂₃C₂ = C₁₄.₄₅2₊¹⁺⁴	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7):23C2	448,1069
(D₄×Dic₇)⋊₂₄C₂ = C₁₄.₄₆2₊¹⁺⁴	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	112	(D4xDic7):24C2	448,1070
(D₄×Dic₇)⋊₂₅C₂ = C₁₄.₁₁₅2₊¹⁺⁴	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7):25C2	448,1071
(D₄×Dic₇)⋊₂₆C₂ = C₁₄.₄₇2₊¹⁺⁴	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7):26C2	448,1072
(D₄×Dic₇)⋊₂₇C₂ = C₄⋊C₄.₁₉₇D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7):27C2	448,1102
(D₄×Dic₇)⋊₂₈C₂ = C₁₄.₁₂₂2₊¹⁺⁴	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	112	(D4xDic7):28C2	448,1111
(D₄×Dic₇)⋊₂₉C₂ = C₁₄.₈₅2_-¹⁺⁴	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7):29C2	448,1118
(D₄×Dic₇)⋊₃₀C₂ = C₄².₂₃₄D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7):30C2	448,1133
(D₄×Dic₇)⋊₃₁C₂ = C₄².₁₄₃D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7):31C2	448,1134
(D₄×Dic₇)⋊₃₂C₂ = C₄².₁₄₄D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7):32C2	448,1135
(D₄×Dic₇)⋊₃₃C₂ = C₄².₁₆₆D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7):33C2	448,1166
(D₄×Dic₇)⋊₃₄C₂ = C₄².₂₃₈D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7):34C2	448,1169
(D₄×Dic₇)⋊₃₅C₂ = Dic₁₄⋊₁₁D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7):35C2	448,1171
(D₄×Dic₇)⋊₃₆C₂ = C₄².₁₆₈D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7):36C2	448,1172
(D₄×Dic₇)⋊₃₇C₂ = C₂⁴.₃₈D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	112	(D4xDic7):37C2	448,1251
(D₄×Dic₇)⋊₃₈C₂ = D₄×C₇⋊D₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	112	(D4xDic7):38C2	448,1254
(D₄×Dic₇)⋊₃₉C₂ = C₂⁴.₄₂D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	112	(D4xDic7):39C2	448,1259
(D₄×Dic₇)⋊₄₀C₂ = C₁₄.₁₀₄2_-¹⁺⁴	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7):40C2	448,1277
(D₄×Dic₇)⋊₄₁C₂ = C₁₄.₁₀₆2_-¹⁺⁴	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7):41C2	448,1280
(D₄×Dic₇)⋊₄₂C₂ = C₁₄.₁₄₅2₊¹⁺⁴	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	112	(D4xDic7):42C2	448,1282
(D₄×Dic₇)⋊₄₃C₂ = C₄×D₄⋊₂D₇	φ: trivial image	224	(D4xDic7):43C2	448,989
(D₄×Dic₇)⋊₄₄C₂ = C₄×D₄×D₇	φ: trivial image	112	(D4xDic7):44C2	448,997
(D₄×Dic₇)⋊₄₅C₂ = C₄○D₄×Dic₇	φ: trivial image	224	(D4xDic7):45C2	448,1279

Non-split extensions G=N.Q with N=D₄×Dic₇ and Q=C₂

extension	φ:Q→Out N	d	Label	ID
(D₄×Dic₇).₁C₂ = D₄.D₇⋊C₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7).1C2	448,291
(D₄×Dic₇).₂C₂ = Dic₇⋊₆SD₁₆	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7).2C2	448,292
(D₄×Dic₇).₃C₂ = Dic₇.D₈	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7).3C2	448,293
(D₄×Dic₇).₄C₂ = D₄⋊Dic₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7).4C2	448,295
(D₄×Dic₇).₅C₂ = D₄.Dic₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7).5C2	448,297
(D₄×Dic₇).₆C₂ = D₄.₂Dic₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7).6C2	448,300
(D₄×Dic₇).₇C₂ = SD₁₆×Dic₇	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7).7C2	448,695
(D₄×Dic₇).₈C₂ = Dic₇⋊₃SD₁₆	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7).8C2	448,696
(D₄×Dic₇).₉C₂ = SD₁₆⋊Dic₇	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7).9C2	448,698
(D₄×Dic₇).₁₀C₂ = D₄×Dic₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7).10C2	448,990
(D₄×Dic₇).₁₁C₂ = D₄⋊₅Dic₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7).11C2	448,992
(D₄×Dic₇).₁₂C₂ = D₄⋊₆Dic₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7).12C2	448,996
(D₄×Dic₇).₁₃C₂ = C₁₄.₈₀2_-¹⁺⁴	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7).13C2	448,1103
(D₄×Dic₇).₁₄C₂ = C₄².₁₃₉D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₄×Dic₇	224	(D4xDic7).14C2	448,1124

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=D4×Dic7 and Q=C2

Extensions 1→N→G→Q→1 with N=D₄×Dic₇ and Q=C₂