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

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

		d	ρ	Label	ID
C₂×C₄³		128		C2xC4^3	128,997

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊₁(C₂×C₄²) = D₄×C₄²	φ: C₂×C₄²/C₄² → C₂ ⊆ Aut C₄	64		C4:1(C2xC4^2)	128,1003
C₄⋊₂(C₂×C₄²) = C₂×C₄×C₄⋊C₄	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₄	128		C4:2(C2xC4^2)	128,1001

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁(C₂×C₄²) = C₄×C₄≀C₂	φ: C₂×C₄²/C₄² → C₂ ⊆ Aut C₄	32		C4.1(C2xC4^2)	128,490
C₄.₂(C₂×C₄²) = D₄.C₄²	φ: C₂×C₄²/C₄² → C₂ ⊆ Aut C₄	32		C4.2(C2xC4^2)	128,491
C₄.₃(C₂×C₄²) = C₄×D₄⋊C₄	φ: C₂×C₄²/C₄² → C₂ ⊆ Aut C₄	64		C4.3(C2xC4^2)	128,492
C₄.₄(C₂×C₄²) = C₄×Q₈⋊C₄	φ: C₂×C₄²/C₄² → C₂ ⊆ Aut C₄	128		C4.4(C2xC4^2)	128,493
C₄.₅(C₂×C₄²) = D₄⋊C₄²	φ: C₂×C₄²/C₄² → C₂ ⊆ Aut C₄	64		C4.5(C2xC4^2)	128,494
C₄.₆(C₂×C₄²) = Q₈⋊C₄²	φ: C₂×C₄²/C₄² → C₂ ⊆ Aut C₄	128		C4.6(C2xC4^2)	128,495
C₄.₇(C₂×C₄²) = Q₈.C₄²	φ: C₂×C₄²/C₄² → C₂ ⊆ Aut C₄	32		C4.7(C2xC4^2)	128,496
C₄.₈(C₂×C₄²) = D₄.₃C₄²	φ: C₂×C₄²/C₄² → C₂ ⊆ Aut C₄	32		C4.8(C2xC4^2)	128,497
C₄.₉(C₂×C₄²) = Q₈×C₄²	φ: C₂×C₄²/C₄² → C₂ ⊆ Aut C₄	128		C4.9(C2xC4^2)	128,1004
C₄.₁₀(C₂×C₄²) = D₄⋊₄C₄²	φ: C₂×C₄²/C₄² → C₂ ⊆ Aut C₄	64		C4.10(C2xC4^2)	128,1007
C₄.₁₁(C₂×C₄²) = Q₈⋊₄C₄²	φ: C₂×C₄²/C₄² → C₂ ⊆ Aut C₄	128		C4.11(C2xC4^2)	128,1008
C₄.₁₂(C₂×C₄²) = C₄×C₈○D₄	φ: C₂×C₄²/C₄² → C₂ ⊆ Aut C₄	64		C4.12(C2xC4^2)	128,1606
C₄.₁₃(C₂×C₄²) = D₄.₅C₄²	φ: C₂×C₄²/C₄² → C₂ ⊆ Aut C₄	64		C4.13(C2xC4^2)	128,1607
C₄.₁₄(C₂×C₄²) = C₂×C₄²⋊₆C₄	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₄	32		C4.14(C2xC4^2)	128,464
C₄.₁₅(C₂×C₄²) = C₂⁴.₆₃D₄	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₄	32		C4.15(C2xC4^2)	128,465
C₄.₁₆(C₂×C₄²) = C₂×C₂².₄Q₁₆	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₄	128		C4.16(C2xC4^2)	128,466
C₄.₁₇(C₂×C₄²) = C₂⁴.₁₃₂D₄	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₄	64		C4.17(C2xC4^2)	128,467
C₄.₁₈(C₂×C₄²) = C₂⁴.₁₅₂D₄	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₄	64		C4.18(C2xC4^2)	128,468
C₄.₁₉(C₂×C₄²) = C₂×C₄.C₄²	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₄	64		C4.19(C2xC4^2)	128,469
C₄.₂₀(C₂×C₄²) = C₂⁴.₇Q₈	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₄	32		C4.20(C2xC4^2)	128,470
C₄.₂₁(C₂×C₄²) = C₈.₁₄C₄²	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₄	32		C4.21(C2xC4^2)	128,504
C₄.₂₂(C₂×C₄²) = C₈.₅C₄²	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₄	32		C4.22(C2xC4^2)	128,505
C₄.₂₃(C₂×C₄²) = C₄×C₄.Q₈	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₄	128		C4.23(C2xC4^2)	128,506
C₄.₂₄(C₂×C₄²) = C₄×C₂.D₈	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₄	128		C4.24(C2xC4^2)	128,507
C₄.₂₅(C₂×C₄²) = C₈⋊C₄²	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₄	128		C4.25(C2xC4^2)	128,508
C₄.₂₆(C₂×C₄²) = C₄×C₈.C₄	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₄	64		C4.26(C2xC4^2)	128,509
C₄.₂₇(C₂×C₄²) = C₈.₆C₄²	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₄	64		C4.27(C2xC4^2)	128,510
C₄.₂₈(C₂×C₄²) = C₄×C₄²⋊C₂	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₄	64		C4.28(C2xC4^2)	128,1002
C₄.₂₉(C₂×C₄²) = C₂⁴.₅₂₄C₂³	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₄	64		C4.29(C2xC4^2)	128,1006
C₄.₃₀(C₂×C₄²) = C₂×C₄×M₄(2)	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₄	64		C4.30(C2xC4^2)	128,1603
C₄.₃₁(C₂×C₄²) = C₂×C₈○₂M₄(2)	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₄	64		C4.31(C2xC4^2)	128,1604
C₄.₃₂(C₂×C₄²) = M₄(2)○₂M₄(2)	φ: C₂×C₄²/C₂²×C₄ → C₂ ⊆ Aut C₄	32		C4.32(C2xC4^2)	128,1605
C₄.₃₃(C₂×C₄²) = C₄×C₈⋊C₄	central extension (φ=1)	128		C4.33(C2xC4^2)	128,457
C₄.₃₄(C₂×C₄²) = C₂.C₄³	central extension (φ=1)	128		C4.34(C2xC4^2)	128,458
C₄.₃₅(C₂×C₄²) = C₂×C₁₆⋊₅C₄	central extension (φ=1)	128		C4.35(C2xC4^2)	128,838
C₄.₃₆(C₂×C₄²) = C₄×M₅(2)	central extension (φ=1)	64		C4.36(C2xC4^2)	128,839
C₄.₃₇(C₂×C₄²) = C₁₆○₂M₅(2)	central extension (φ=1)	64		C4.37(C2xC4^2)	128,840
C₄.₃₈(C₂×C₄²) = C₂×C₄²⋊₄C₄	central extension (φ=1)	128		C4.38(C2xC4^2)	128,999
C₄.₃₉(C₂×C₄²) = C₂²×C₈⋊C₄	central extension (φ=1)	128		C4.39(C2xC4^2)	128,1602
C₄.₄₀(C₂×C₄²) = C₂×C₄.₉C₄²	central stem extension (φ=1)	32		C4.40(C2xC4^2)	128,462
C₄.₄₁(C₂×C₄²) = C₂×C₄.₁₀C₄²	central stem extension (φ=1)	32		C4.41(C2xC4^2)	128,463
C₄.₄₂(C₂×C₄²) = C₈.₁₆C₄²	central stem extension (φ=1)	32	4	C4.42(C2xC4^2)	128,479
C₄.₄₃(C₂×C₄²) = C₂×C₁₆⋊C₄	central stem extension (φ=1)	32		C4.43(C2xC4^2)	128,841
C₄.₄₄(C₂×C₄²) = C₈.₂₃C₄²	central stem extension (φ=1)	32	4	C4.44(C2xC4^2)	128,842

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

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