Extensions 1→N→G→Q→1 with N=C₄²⋊₆C₄ and Q=C₂

Direct product G=N×Q with N=C₄²⋊₆C₄ and Q=C₂

		d	ρ	Label	ID
C₂×C₄²⋊₆C₄		32		C2xC4^2:6C4	128,464

Semidirect products G=N:Q with N=C₄²⋊₆C₄ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
C₄²⋊₆C₄⋊₁C₂ = C₂⁴.₂₁D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	32		C4^2:6C4:1C2	128,588
C₄²⋊₆C₄⋊₂C₂ = C₈.C₂²⋊C₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	32		C4^2:6C4:2C2	128,614
C₄²⋊₆C₄⋊₃C₂ = C₈⋊C₂²⋊C₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	32		C4^2:6C4:3C2	128,615
C₄²⋊₆C₄⋊₄C₂ = C₄².₄₂₆D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	16	4	C4^2:6C4:4C2	128,638
C₄²⋊₆C₄⋊₅C₂ = C₄².₄₂₇D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	16	4	C4^2:6C4:5C2	128,664
C₄²⋊₆C₄⋊₆C₂ = C₄²⋊₉D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	16		C4^2:6C4:6C2	128,734
C₄²⋊₆C₄⋊₇C₂ = C₄².₁₂₉D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	32		C4^2:6C4:7C2	128,735
C₄²⋊₆C₄⋊₈C₂ = C₄²⋊₁₀D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	32		C4^2:6C4:8C2	128,736
C₄²⋊₆C₄⋊₉C₂ = C₄².₁₃₀D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	32		C4^2:6C4:9C2	128,737
C₄²⋊₆C₄⋊₁₀C₂ = C₂⁴.₆₃D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	32		C4^2:6C4:10C2	128,465
C₄²⋊₆C₄⋊₁₁C₂ = D₄.C₄²	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	32		C4^2:6C4:11C2	128,491
C₄²⋊₆C₄⋊₁₂C₂ = D₄.₃C₄²	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	32		C4^2:6C4:12C2	128,497
C₄²⋊₆C₄⋊₁₃C₂ = C₄².₁₀₂D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	32		C4^2:6C4:13C2	128,538
C₄²⋊₆C₄⋊₁₄C₂ = C₂⁴.₇₀D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	32		C4^2:6C4:14C2	128,558
C₄²⋊₆C₄⋊₁₅C₂ = (C₂×C₄²)⋊C₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	16	4	C4^2:6C4:15C2	128,559
C₄²⋊₆C₄⋊₁₆C₂ = C₄≀C₂⋊C₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	32		C4^2:6C4:16C2	128,591
C₄²⋊₆C₄⋊₁₇C₂ = C₄²⋊₉(C₂×C₄)	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	32		C4^2:6C4:17C2	128,592
C₄²⋊₆C₄⋊₁₈C₂ = M₄(2).₄₁D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	16	4	C4^2:6C4:18C2	128,593
C₄²⋊₆C₄⋊₁₉C₂ = M₄(2).₄₂D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	32		C4^2:6C4:19C2	128,598
C₄²⋊₆C₄⋊₂₀C₂ = C₂⁴.₇₂D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	32		C4^2:6C4:20C2	128,603
C₄²⋊₆C₄⋊₂₁C₂ = M₄(2)⋊₁₉D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	16	4	C4^2:6C4:21C2	128,616
C₄²⋊₆C₄⋊₂₂C₂ = C₂⁴.₂₃D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	32		C4^2:6C4:22C2	128,617
C₄²⋊₆C₄⋊₂₃C₂ = C₂⁴.₂₄D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	16		C4^2:6C4:23C2	128,619
C₄²⋊₆C₄⋊₂₄C₂ = C₄.₄D₄⋊₁₃C₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	32		C4^2:6C4:24C2	128,620
C₄²⋊₆C₄⋊₂₅C₂ = (C₂×C₄)≀C₂	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	16		C4^2:6C4:25C2	128,628
C₄²⋊₆C₄⋊₂₆C₂ = C₄²⋊₇D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	32		C4^2:6C4:26C2	128,629
C₄²⋊₆C₄⋊₂₇C₂ = M₄(2).₂₄D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	32		C4^2:6C4:27C2	128,661
C₄²⋊₆C₄⋊₂₈C₂ = C₄².₄₂₈D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	32		C4^2:6C4:28C2	128,669
C₄²⋊₆C₄⋊₂₉C₂ = C₄².₁₀₇D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	32		C4^2:6C4:29C2	128,670
C₄²⋊₆C₄⋊₃₀C₂ = (C₂×D₄)⋊₂Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	32		C4^2:6C4:30C2	128,759
C₄²⋊₆C₄⋊₃₁C₂ = C₄².₈D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	16	4	C4^2:6C4:31C2	128,763
C₄²⋊₆C₄⋊₃₂C₂ = M₄(2)⋊₆D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	32		C4^2:6C4:32C2	128,769
C₄²⋊₆C₄⋊₃₃C₂ = M₄(2).₇D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	32		C4^2:6C4:33C2	128,770
C₄²⋊₆C₄⋊₃₄C₂ = C₄×C₄≀C₂	φ: trivial image	32		C4^2:6C4:34C2	128,490
C₄²⋊₆C₄⋊₃₅C₂ = Q₈.C₄²	φ: trivial image	32		C4^2:6C4:35C2	128,496

Non-split extensions G=N.Q with N=C₄²⋊₆C₄ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
C₄²⋊₆C₄.₁C₂ = C₄.₁₀D₄⋊₂C₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	32		C4^2:6C4.1C2	128,589
C₄²⋊₆C₄.₂C₂ = M₄(2)⋊Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	32		C4^2:6C4.2C2	128,792
C₄²⋊₆C₄.₃C₂ = C₄²⋊₃Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	32		C4^2:6C4.3C2	128,793
C₄²⋊₆C₄.₄C₂ = C₈.₅C₄²	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	32		C4^2:6C4.4C2	128,505
C₄²⋊₆C₄.₅C₂ = C₈⋊C₄⋊₁₇C₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	16	4	C4^2:6C4.5C2	128,573
C₄²⋊₆C₄.₆C₂ = C₄⋊Q₈⋊₁₅C₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	32		C4^2:6C4.6C2	128,618
C₄²⋊₆C₄.₇C₂ = M₄(2).₃Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	32		C4^2:6C4.7C2	128,654
C₄²⋊₆C₄.₈C₂ = C₄².₆₂Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	32		C4^2:6C4.8C2	128,677
C₄²⋊₆C₄.₉C₂ = C₄².₂₈Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	32		C4^2:6C4.9C2	128,678
C₄²⋊₆C₄.₁₀C₂ = M₄(2)⋊₇Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	32		C4^2:6C4.10C2	128,718
C₄²⋊₆C₄.₁₁C₂ = C₄²⋊₁₆Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	32		C4^2:6C4.11C2	128,726
C₄²⋊₆C₄.₁₂C₂ = C₄²⋊Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	32		C4^2:6C4.12C2	128,727
C₄²⋊₆C₄.₁₃C₂ = (C₂×Q₈)⋊₂Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	32		C4^2:6C4.13C2	128,760
C₄²⋊₆C₄.₁₄C₂ = C₄².₃₂Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₆C₄	16	4	C4^2:6C4.14C2	128,834
C₄²⋊₆C₄.₁₅C₂ = C₈.₁₄C₄²	φ: trivial image	32		C4^2:6C4.15C2	128,504

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Extensions 1→N→G→Q→1 with N=C42⋊6C4 and Q=C2

Extensions 1→N→G→Q→1 with N=C₄²⋊₆C₄ and Q=C₂