Extensions 1→N→G→Q→1 with N=C₂²×C₄² and Q=C₂

Direct product G=N×Q with N=C₂²×C₄² and Q=C₂

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

Semidirect products G=N:Q with N=C₂²×C₄² and Q=C₂

extension	φ:Q→Aut N	d	Label	ID
(C₂²×C₄²)⋊₁C₂ = C₂³⋊₂C₄²	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2):1C2	128,169
(C₂²×C₄²)⋊₂C₂ = C₂×C₄×C₂²⋊C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2):2C2	128,1000
(C₂²×C₄²)⋊₃C₂ = D₄×C₄²	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2):3C2	128,1003
(C₂²×C₄²)⋊₄C₂ = C₂×C₂⁴.C₂²	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2):4C2	128,1021
(C₂²×C₄²)⋊₅C₂ = C₄²⋊₄₂D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2):5C2	128,1022
(C₂²×C₄²)⋊₆C₂ = C₄×C₂².D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2):6C2	128,1033
(C₂²×C₄²)⋊₇C₂ = C₄²⋊₄₃D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2):7C2	128,1584
(C₂²×C₄²)⋊₈C₂ = C₂³.₇₅₃C₂⁴	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2):8C2	128,1585
(C₂²×C₄²)⋊₉C₂ = C₂²×C₄²⋊C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2):9C2	128,2153
(C₂²×C₄²)⋊₁₀C₂ = C₂²×C₄²⋊₂C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2):10C2	128,2170
(C₂²×C₄²)⋊₁₁C₂ = (C₂×C₄)≀C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	16	(C2^2xC4^2):11C2	128,628
(C₂²×C₄²)⋊₁₂C₂ = C₂×C₂⁴.₃C₂²	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2):12C2	128,1024
(C₂²×C₄²)⋊₁₃C₂ = C₂³.₁₇₉C₂⁴	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2):13C2	128,1029
(C₂²×C₄²)⋊₁₄C₂ = C₄×C₄⋊D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2):14C2	128,1032
(C₂²×C₄²)⋊₁₅C₂ = C₄²⋊₄₆D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2):15C2	128,1582
(C₂²×C₄²)⋊₁₆C₂ = C₂⁴.₅₉₈C₂³	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2):16C2	128,1586
(C₂²×C₄²)⋊₁₇C₂ = C₄²⋊₄₇D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2):17C2	128,1588
(C₂²×C₄²)⋊₁₈C₂ = C₂²×C₄≀C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	32	(C2^2xC4^2):18C2	128,1631
(C₂²×C₄²)⋊₁₉C₂ = D₄×C₂²×C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2):19C2	128,2154
(C₂²×C₄²)⋊₂₀C₂ = C₂×C₄×C₄○D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2):20C2	128,2156
(C₂²×C₄²)⋊₂₁C₂ = C₂²×C₄.₄D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2):21C2	128,2168
(C₂²×C₄²)⋊₂₂C₂ = C₂×C₂³.₃₆C₂³	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2):22C2	128,2171
(C₂²×C₄²)⋊₂₃C₂ = C₂²×C₄⋊₁D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2):23C2	128,2172
(C₂²×C₄²)⋊₂₄C₂ = C₂×C₂².₂₆C₂⁴	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2):24C2	128,2174
(C₂²×C₄²)⋊₂₅C₂ = C₂².₃₃C₂⁵	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	32	(C2^2xC4^2):25C2	128,2176

Non-split extensions G=N.Q with N=C₂²×C₄² and Q=C₂

extension	φ:Q→Aut N	d	Label	ID
(C₂²×C₄²).₁C₂ = C₄×C₂.C₄²	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	128	(C2^2xC4^2).1C2	128,164
(C₂²×C₄²).₂C₂ = C₂⁴.₆₂₄C₂³	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	128	(C2^2xC4^2).2C2	128,166
(C₂²×C₄²).₃C₂ = C₂⁴.₆₂₆C₂³	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	128	(C2^2xC4^2).3C2	128,168
(C₂²×C₄²).₄C₂ = C₂×C₂².₇C₄²	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	128	(C2^2xC4^2).4C2	128,459
(C₂²×C₄²).₅C₂ = C₄×C₂²⋊C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2).5C2	128,480
(C₂²×C₄²).₆C₂ = C₄².₃₇₈D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2).6C2	128,481
(C₂²×C₄²).₇C₂ = C₂³.₃₂M₄(2)	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2).7C2	128,549
(C₂²×C₄²).₈C₂ = C₂×C₄²⋊₄C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	128	(C2^2xC4^2).8C2	128,999
(C₂²×C₄²).₉C₂ = C₂×C₄×C₄⋊C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	128	(C2^2xC4^2).9C2	128,1001
(C₂²×C₄²).₁₀C₂ = C₂×C₄²⋊₅C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	128	(C2^2xC4^2).10C2	128,1014
(C₂²×C₄²).₁₁C₂ = C₂×C₂³.₆₃C₂³	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	128	(C2^2xC4^2).11C2	128,1020
(C₂²×C₄²).₁₂C₂ = C₂²×C₈⋊C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	128	(C2^2xC4^2).12C2	128,1602
(C₂²×C₄²).₁₃C₂ = C₂⁴.₆₂₅C₂³	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	128	(C2^2xC4^2).13C2	128,167
(C₂²×C₄²).₁₄C₂ = C₂³.₂₈C₄²	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2).14C2	128,460
(C₂²×C₄²).₁₅C₂ = C₂×C₄²⋊₆C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	32	(C2^2xC4^2).15C2	128,464
(C₂²×C₄²).₁₆C₂ = C₄².₄₂₅D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2).16C2	128,529
(C₂²×C₄²).₁₇C₂ = C₄×C₄²⋊C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2).17C2	128,1002
(C₂²×C₄²).₁₈C₂ = C₂×C₄²⋊₈C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	128	(C2^2xC4^2).18C2	128,1013
(C₂²×C₄²).₁₉C₂ = C₂³.₁₆₅C₂⁴	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2).19C2	128,1015
(C₂²×C₄²).₂₀C₂ = C₂×C₄²⋊₉C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	128	(C2^2xC4^2).20C2	128,1016
(C₂²×C₄²).₂₁C₂ = C₂³.₁₆₇C₂⁴	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2).21C2	128,1017
(C₂²×C₄²).₂₂C₂ = C₂×C₂³.₆₅C₂³	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	128	(C2^2xC4^2).22C2	128,1023
(C₂²×C₄²).₂₃C₂ = C₂×C₂³.₆₇C₂³	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	128	(C2^2xC4^2).23C2	128,1026
(C₂²×C₄²).₂₄C₂ = C₂³.₁₇₈C₂⁴	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2).24C2	128,1028
(C₂²×C₄²).₂₅C₂ = C₄×C₂²⋊Q₈	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2).25C2	128,1034
(C₂²×C₄²).₂₆C₂ = C₄².₄₃₉D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2).26C2	128,1583
(C₂²×C₄²).₂₇C₂ = C₂⁴.₅₉₉C₂³	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2).27C2	128,1587
(C₂²×C₄²).₂₈C₂ = C₄².₄₄₀D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2).28C2	128,1589
(C₂²×C₄²).₂₉C₂ = C₂×C₄×M₄(2)	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2).29C2	128,1603
(C₂²×C₄²).₃₀C₂ = C₂²×C₄⋊C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	128	(C2^2xC4^2).30C2	128,1634
(C₂²×C₄²).₃₁C₂ = C₂×C₄⋊M₄(2)	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2).31C2	128,1635
(C₂²×C₄²).₃₂C₂ = C₂×C₄².₁₂C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2).32C2	128,1649
(C₂²×C₄²).₃₃C₂ = C₂×C₄².₆C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2).33C2	128,1650
(C₂²×C₄²).₃₄C₂ = C₄².₆₇₇C₂³	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	32	(C2^2xC4^2).34C2	128,1652
(C₂²×C₄²).₃₅C₂ = Q₈×C₂²×C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	128	(C2^2xC4^2).35C2	128,2155
(C₂²×C₄²).₃₆C₂ = C₂²×C₄².C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	128	(C2^2xC4^2).36C2	128,2169
(C₂²×C₄²).₃₇C₂ = C₂²×C₄⋊Q₈	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	128	(C2^2xC4^2).37C2	128,2173
(C₂²×C₄²).₃₈C₂ = C₂×C₂³.₃₇C₂³	φ: C₂/C₁ → C₂ ⊆ Aut C₂²×C₄²	64	(C2^2xC4^2).38C2	128,2175

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Extensions 1→N→G→Q→1 with N=C22×C42 and Q=C2

Extensions 1→N→G→Q→1 with N=C₂²×C₄² and Q=C₂