Extensions 1→N→G→Q→1 with N=C₂³×C₄ and Q=C₄

Direct product G=N×Q with N=C₂³×C₄ and Q=C₄

		d	ρ	Label	ID
C₂³×C₄²		128		C2^3xC4^2	128,2150

Semidirect products G=N:Q with N=C₂³×C₄ and Q=C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂³×C₄)⋊₁C₄ = C₂⁴.₅D₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂³×C₄	32		(C2^3xC4):1C4	128,122
(C₂³×C₄)⋊₂C₄ = C₂×C₂³.₉D₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂³×C₄	32		(C2^3xC4):2C4	128,471
(C₂³×C₄)⋊₃C₄ = C₄×C₂³⋊C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂³×C₄	32		(C2^3xC4):3C4	128,486
(C₂³×C₄)⋊₄C₄ = C₂⁴.₆₈D₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂³×C₄	16		(C2^3xC4):4C4	128,551
(C₂³×C₄)⋊₅C₄ = C₂×C₂³.D₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂³×C₄	32		(C2^3xC4):5C4	128,851
(C₂³×C₄)⋊₆C₄ = C₂⁵⋊C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂³×C₄	16		(C2^3xC4):6C4	128,513
(C₂³×C₄)⋊₇C₄ = C₂⁴.₁₆₅C₂³	φ: C₄/C₁ → C₄ ⊆ Aut C₂³×C₄	32		(C2^3xC4):7C4	128,514
(C₂³×C₄)⋊₈C₄ = C₂⁴.₁₆₇C₂³	φ: C₄/C₁ → C₄ ⊆ Aut C₂³×C₄	32		(C2^3xC4):8C4	128,531
(C₂³×C₄)⋊₉C₄ = C₄○C₂≀C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂³×C₄	16	4	(C2^3xC4):9C4	128,852
(C₂³×C₄)⋊₁₀C₄ = C₂²×C₂³⋊C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂³×C₄	32		(C2^3xC4):10C4	128,1613
(C₂³×C₄)⋊₁₁C₄ = C₂×C₂³.C₂³	φ: C₄/C₁ → C₄ ⊆ Aut C₂³×C₄	32		(C2^3xC4):11C4	128,1614
(C₂³×C₄)⋊₁₂C₄ = C₂⁴.₁₇Q₈	φ: C₄/C₂ → C₂ ⊆ Aut C₂³×C₄	64		(C2^3xC4):12C4	128,165
(C₂³×C₄)⋊₁₃C₄ = C₂²×C₂.C₄²	φ: C₄/C₂ → C₂ ⊆ Aut C₂³×C₄	128		(C2^3xC4):13C4	128,998
(C₂³×C₄)⋊₁₄C₄ = C₂×C₄×C₂²⋊C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₂³×C₄	64		(C2^3xC4):14C4	128,1000
(C₂³×C₄)⋊₁₅C₄ = C₂×C₂³.₃₄D₄	φ: C₄/C₂ → C₂ ⊆ Aut C₂³×C₄	64		(C2^3xC4):15C4	128,1011
(C₂³×C₄)⋊₁₆C₄ = C₂×C₂³.₇Q₈	φ: C₄/C₂ → C₂ ⊆ Aut C₂³×C₄	64		(C2^3xC4):16C4	128,1010
(C₂³×C₄)⋊₁₇C₄ = C₂⁵.₈₅C₂²	φ: C₄/C₂ → C₂ ⊆ Aut C₂³×C₄	32		(C2^3xC4):17C4	128,1012
(C₂³×C₄)⋊₁₈C₄ = C₂³×C₄⋊C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₂³×C₄	128		(C2^3xC4):18C4	128,2152
(C₂³×C₄)⋊₁₉C₄ = C₂²×C₄²⋊C₂	φ: C₄/C₂ → C₂ ⊆ Aut C₂³×C₄	64		(C2^3xC4):19C4	128,2153

Non-split extensions G=N.Q with N=C₂³×C₄ and Q=C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂³×C₄).₁C₄ = C₂³.₁₉C₄²	φ: C₄/C₁ → C₄ ⊆ Aut C₂³×C₄	64		(C2^3xC4).1C4	128,12
(C₂³×C₄).₂C₄ = C₂³⋊C₁₆	φ: C₄/C₁ → C₄ ⊆ Aut C₂³×C₄	32		(C2^3xC4).2C4	128,46
(C₂³×C₄).₃C₄ = C₂³.₁₅M₄(2)	φ: C₄/C₁ → C₄ ⊆ Aut C₂³×C₄	32		(C2^3xC4).3C4	128,49
(C₂³×C₄).₄C₄ = C₂³.₂M₄(2)	φ: C₄/C₁ → C₄ ⊆ Aut C₂³×C₄	32		(C2^3xC4).4C4	128,58
(C₂³×C₄).₅C₄ = C₂×C₂³⋊C₈	φ: C₄/C₁ → C₄ ⊆ Aut C₂³×C₄	32		(C2^3xC4).5C4	128,188
(C₂³×C₄).₆C₄ = C₂³.₈M₄(2)	φ: C₄/C₁ → C₄ ⊆ Aut C₂³×C₄	32		(C2^3xC4).6C4	128,191
(C₂³×C₄).₇C₄ = C₄².₃₉₃D₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂³×C₄	32		(C2^3xC4).7C4	128,192
(C₂³×C₄).₈C₄ = C₂⁵.₃C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂³×C₄	16		(C2^3xC4).8C4	128,194
(C₂³×C₄).₉C₄ = C₂×C₂².C₄²	φ: C₄/C₁ → C₄ ⊆ Aut C₂³×C₄	64		(C2^3xC4).9C4	128,473
(C₂³×C₄).₁₀C₄ = C₄×C₄.D₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂³×C₄	32		(C2^3xC4).10C4	128,487
(C₂³×C₄).₁₁C₄ = (C₂²×C₄).₂₇₅D₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂³×C₄	32		(C2^3xC4).11C4	128,553
(C₂³×C₄).₁₂C₄ = C₂⁴.C₈	φ: C₄/C₁ → C₄ ⊆ Aut C₂³×C₄	16	4	(C2^3xC4).12C4	128,52
(C₂³×C₄).₁₃C₄ = C₂×C₂².M₄(2)	φ: C₄/C₁ → C₄ ⊆ Aut C₂³×C₄	64		(C2^3xC4).13C4	128,189
(C₂³×C₄).₁₄C₄ = C₄².₃₇₁D₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂³×C₄	32		(C2^3xC4).14C4	128,190
(C₂³×C₄).₁₅C₄ = (C₂×C₄)⋊M₄(2)	φ: C₄/C₁ → C₄ ⊆ Aut C₂³×C₄	32		(C2^3xC4).15C4	128,195
(C₂³×C₄).₁₆C₄ = C₄².₄₂D₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂³×C₄	32		(C2^3xC4).16C4	128,196
(C₂³×C₄).₁₇C₄ = C₂³⋊M₄(2)	φ: C₄/C₁ → C₄ ⊆ Aut C₂³×C₄	32		(C2^3xC4).17C4	128,197
(C₂³×C₄).₁₈C₄ = C₄².₄₃D₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂³×C₄	32		(C2^3xC4).18C4	128,198
(C₂³×C₄).₁₉C₄ = C₄.C₂²≀C₂	φ: C₄/C₁ → C₄ ⊆ Aut C₂³×C₄	32		(C2^3xC4).19C4	128,516
(C₂³×C₄).₂₀C₄ = (C₂³×C₄).C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂³×C₄	32		(C2^3xC4).20C4	128,517
(C₂³×C₄).₂₁C₄ = C₄².₉₆D₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂³×C₄	32		(C2^3xC4).21C4	128,532
(C₂³×C₄).₂₂C₄ = C₂×C₂³.C₈	φ: C₄/C₁ → C₄ ⊆ Aut C₂³×C₄	32		(C2^3xC4).22C4	128,846
(C₂³×C₄).₂₃C₄ = C₂²×C₄.₁₀D₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂³×C₄	64		(C2^3xC4).23C4	128,1618
(C₂³×C₄).₂₄C₄ = C₂×M₄(2).₈C₂²	φ: C₄/C₁ → C₄ ⊆ Aut C₂³×C₄	32		(C2^3xC4).24C4	128,1619
(C₂³×C₄).₂₅C₄ = C₂×C₂².₇C₄²	φ: C₄/C₂ → C₂ ⊆ Aut C₂³×C₄	128		(C2^3xC4).25C4	128,459
(C₂³×C₄).₂₆C₄ = C₂³.₂₈C₄²	φ: C₄/C₂ → C₂ ⊆ Aut C₂³×C₄	64		(C2^3xC4).26C4	128,460
(C₂³×C₄).₂₇C₄ = C₄×C₂²⋊C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₂³×C₄	64		(C2^3xC4).27C4	128,480
(C₂³×C₄).₂₈C₄ = C₄².₃₇₈D₄	φ: C₄/C₂ → C₂ ⊆ Aut C₂³×C₄	64		(C2^3xC4).28C4	128,481
(C₂³×C₄).₂₉C₄ = C₂⁴⋊₃C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₂³×C₄	32		(C2^3xC4).29C4	128,511
(C₂³×C₄).₃₀C₄ = C₂³.₃₂M₄(2)	φ: C₄/C₂ → C₂ ⊆ Aut C₂³×C₄	64		(C2^3xC4).30C4	128,549
(C₂³×C₄).₃₁C₄ = C₂×C₂²⋊C₁₆	φ: C₄/C₂ → C₂ ⊆ Aut C₂³×C₄	64		(C2^3xC4).31C4	128,843
(C₂³×C₄).₃₂C₄ = C₂²×C₈⋊C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₂³×C₄	128		(C2^3xC4).32C4	128,1602
(C₂³×C₄).₃₃C₄ = C₂×C₄×M₄(2)	φ: C₄/C₂ → C₂ ⊆ Aut C₂³×C₄	64		(C2^3xC4).33C4	128,1603
(C₂³×C₄).₃₄C₄ = C₂²×C₂²⋊C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₂³×C₄	64		(C2^3xC4).34C4	128,1608
(C₂³×C₄).₃₅C₄ = C₂×C₄².₆C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₂³×C₄	64		(C2^3xC4).35C4	128,1650
(C₂³×C₄).₃₆C₄ = C₄².₄₂₅D₄	φ: C₄/C₂ → C₂ ⊆ Aut C₂³×C₄	64		(C2^3xC4).36C4	128,529
(C₂³×C₄).₃₇C₄ = C₂⁴.₅C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₂³×C₄	32		(C2^3xC4).37C4	128,844
(C₂³×C₄).₃₈C₄ = C₂×C₂⁴.₄C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₂³×C₄	32		(C2^3xC4).38C4	128,1609
(C₂³×C₄).₃₉C₄ = C₂²×C₄⋊C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₂³×C₄	128		(C2^3xC4).39C4	128,1634
(C₂³×C₄).₄₀C₄ = C₂×C₄⋊M₄(2)	φ: C₄/C₂ → C₂ ⊆ Aut C₂³×C₄	64		(C2^3xC4).40C4	128,1635
(C₂³×C₄).₄₁C₄ = C₂×C₄².₁₂C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₂³×C₄	64		(C2^3xC4).41C4	128,1649
(C₂³×C₄).₄₂C₄ = C₄².₆₇₇C₂³	φ: C₄/C₂ → C₂ ⊆ Aut C₂³×C₄	32		(C2^3xC4).42C4	128,1652
(C₂³×C₄).₄₃C₄ = C₂²×M₅(2)	φ: C₄/C₂ → C₂ ⊆ Aut C₂³×C₄	64		(C2^3xC4).43C4	128,2137
(C₂³×C₄).₄₄C₄ = C₂³×M₄(2)	φ: C₄/C₂ → C₂ ⊆ Aut C₂³×C₄	64		(C2^3xC4).44C4	128,2302

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Extensions 1→N→G→Q→1 with N=C23×C4 and Q=C4

Extensions 1→N→G→Q→1 with N=C₂³×C₄ and Q=C₄