Extensions 1→N→G→Q→1 with N=C₂×C₄ and Q=C₂²

Direct product G=N×Q with N=C₂×C₄ and Q=C₂²

		d	ρ	Label	ID
C₂³×C₄		32		C2^3xC4	32,45

Semidirect products G=N:Q with N=C₂×C₄ and Q=C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₄)⋊₁C₂² = C₂²≀C₂	φ: C₂²/C₁ → C₂² ⊆ Aut C₂×C₄	8		(C2xC4):1C2^2	32,27
(C₂×C₄)⋊₂C₂² = 2₊¹⁺⁴	φ: C₂²/C₁ → C₂² ⊆ Aut C₂×C₄	8	4+	(C2xC4):2C2^2	32,49
(C₂×C₄)⋊₃C₂² = C₂×C₂²⋊C₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₄	16		(C2xC4):3C2^2	32,22
(C₂×C₄)⋊₄C₂² = C₂²×D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₄	16		(C2xC4):4C2^2	32,46
(C₂×C₄)⋊₅C₂² = C₂×C₄○D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₄	16		(C2xC4):5C2^2	32,48

Non-split extensions G=N.Q with N=C₂×C₄ and Q=C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₄).₁C₂² = C₄.D₄	φ: C₂²/C₁ → C₂² ⊆ Aut C₂×C₄	8	4+	(C2xC4).1C2^2	32,7
(C₂×C₄).₂C₂² = C₄.₁₀D₄	φ: C₂²/C₁ → C₂² ⊆ Aut C₂×C₄	16	4-	(C2xC4).2C2^2	32,8
(C₂×C₄).₃C₂² = C₄².C₂	φ: C₂²/C₁ → C₂² ⊆ Aut C₂×C₄	32		(C2xC4).3C2^2	32,32
(C₂×C₄).₄C₂² = C₄²⋊₂C₂	φ: C₂²/C₁ → C₂² ⊆ Aut C₂×C₄	16		(C2xC4).4C2^2	32,33
(C₂×C₄).₅C₂² = C₄⋊Q₈	φ: C₂²/C₁ → C₂² ⊆ Aut C₂×C₄	32		(C2xC4).5C2^2	32,35
(C₂×C₄).₆C₂² = C₈⋊C₂²	φ: C₂²/C₁ → C₂² ⊆ Aut C₂×C₄	8	4+	(C2xC4).6C2^2	32,43
(C₂×C₄).₇C₂² = C₈.C₂²	φ: C₂²/C₁ → C₂² ⊆ Aut C₂×C₄	16	4-	(C2xC4).7C2^2	32,44
(C₂×C₄).₈C₂² = 2_-¹⁺⁴	φ: C₂²/C₁ → C₂² ⊆ Aut C₂×C₄	16	4-	(C2xC4).8C2^2	32,50
(C₂×C₄).₉C₂² = C₂×C₄⋊C₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₄	32		(C2xC4).9C2^2	32,23
(C₂×C₄).₁₀C₂² = C₄²⋊C₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₄	16		(C2xC4).10C2^2	32,24
(C₂×C₄).₁₁C₂² = C₄×D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₄	16		(C2xC4).11C2^2	32,25
(C₂×C₄).₁₂C₂² = C₄×Q₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₄	32		(C2xC4).12C2^2	32,26
(C₂×C₄).₁₃C₂² = C₂².D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₄	16		(C2xC4).13C2^2	32,30
(C₂×C₄).₁₄C₂² = D₄⋊C₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₄	16		(C2xC4).14C2^2	32,9
(C₂×C₄).₁₅C₂² = Q₈⋊C₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₄	32		(C2xC4).15C2^2	32,10
(C₂×C₄).₁₆C₂² = C₄≀C₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₄	8	2	(C2xC4).16C2^2	32,11
(C₂×C₄).₁₇C₂² = C₄.Q₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₄	32		(C2xC4).17C2^2	32,13
(C₂×C₄).₁₈C₂² = C₂.D₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₄	32		(C2xC4).18C2^2	32,14
(C₂×C₄).₁₉C₂² = C₈.C₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₄	16	2	(C2xC4).19C2^2	32,15
(C₂×C₄).₂₀C₂² = C₄⋊D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₄	16		(C2xC4).20C2^2	32,28
(C₂×C₄).₂₁C₂² = C₂²⋊Q₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₄	16		(C2xC4).21C2^2	32,29
(C₂×C₄).₂₂C₂² = C₄.₄D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₄	16		(C2xC4).22C2^2	32,31
(C₂×C₄).₂₃C₂² = C₄⋊₁D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₄	16		(C2xC4).23C2^2	32,34
(C₂×C₄).₂₄C₂² = C₂×M₄(2)	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₄	16		(C2xC4).24C2^2	32,37
(C₂×C₄).₂₅C₂² = C₈○D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₄	16	2	(C2xC4).25C2^2	32,38
(C₂×C₄).₂₆C₂² = C₂×D₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₄	16		(C2xC4).26C2^2	32,39
(C₂×C₄).₂₇C₂² = C₂×SD₁₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₄	16		(C2xC4).27C2^2	32,40
(C₂×C₄).₂₈C₂² = C₂×Q₁₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₄	32		(C2xC4).28C2^2	32,41
(C₂×C₄).₂₉C₂² = C₄○D₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₄	16	2	(C2xC4).29C2^2	32,42
(C₂×C₄).₃₀C₂² = C₂²×Q₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₄	32		(C2xC4).30C2^2	32,47
(C₂×C₄).₃₁C₂² = C₈⋊C₄	central extension (φ=1)	32		(C2xC4).31C2^2	32,4
(C₂×C₄).₃₂C₂² = C₂²⋊C₈	central extension (φ=1)	16		(C2xC4).32C2^2	32,5
(C₂×C₄).₃₃C₂² = C₄⋊C₈	central extension (φ=1)	32		(C2xC4).33C2^2	32,12

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Extensions 1→N→G→Q→1 with N=C2×C4 and Q=C22

Extensions 1→N→G→Q→1 with N=C₂×C₄ and Q=C₂²