Extensions 1→N→G→Q→1 with N=C₄ and Q=C₂³.D₇

Direct product G=N×Q with N=C₄ and Q=C₂³.D₇

		d	ρ	Label	ID
C₄×C₂³.D₇		224		C4xC2^3.D7	448,743

Semidirect products G=N:Q with N=C₄ and Q=C₂³.D₇

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊₁(C₂³.D₇) = C₂⁴.₁₉D₁₄	φ: C₂³.D₇/C₂×Dic₇ → C₂ ⊆ Aut C₄	224		C4:1(C2^3.D7)	448,755
C₄⋊₂(C₂³.D₇) = C₂³.₂₇D₂₈	φ: C₂³.D₇/C₂²×C₁₄ → C₂ ⊆ Aut C₄	224		C4:2(C2^3.D7)	448,746

Non-split extensions G=N.Q with N=C₄ and Q=C₂³.D₇

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁(C₂³.D₇) = C₁₄.SD₃₂	φ: C₂³.D₇/C₂×Dic₇ → C₂ ⊆ Aut C₄	224		C4.1(C2^3.D7)	448,119
C₄.₂(C₂³.D₇) = D₈.Dic₇	φ: C₂³.D₇/C₂×Dic₇ → C₂ ⊆ Aut C₄	112	4	C4.2(C2^3.D7)	448,120
C₄.₃(C₂³.D₇) = C₁₄.Q₃₂	φ: C₂³.D₇/C₂×Dic₇ → C₂ ⊆ Aut C₄	448		C4.3(C2^3.D7)	448,121
C₄.₄(C₂³.D₇) = Q₁₆.Dic₇	φ: C₂³.D₇/C₂×Dic₇ → C₂ ⊆ Aut C₄	224	4	C4.4(C2^3.D7)	448,122
C₄.₅(C₂³.D₇) = D₈⋊₂Dic₇	φ: C₂³.D₇/C₂×Dic₇ → C₂ ⊆ Aut C₄	112	4	C4.5(C2^3.D7)	448,123
C₄.₆(C₂³.D₇) = C₂₈.₅₈D₈	φ: C₂³.D₇/C₂×Dic₇ → C₂ ⊆ Aut C₄	224	4	C4.6(C2^3.D7)	448,124
C₄.₇(C₂³.D₇) = C₂×D₄⋊Dic₇	φ: C₂³.D₇/C₂×Dic₇ → C₂ ⊆ Aut C₄	224		C4.7(C2^3.D7)	448,748
C₄.₈(C₂³.D₇) = (D₄×C₁₄)⋊₆C₄	φ: C₂³.D₇/C₂×Dic₇ → C₂ ⊆ Aut C₄	112		C4.8(C2^3.D7)	448,749
C₄.₉(C₂³.D₇) = C₂×C₂₈.D₄	φ: C₂³.D₇/C₂×Dic₇ → C₂ ⊆ Aut C₄	112		C4.9(C2^3.D7)	448,750
C₄.₁₀(C₂³.D₇) = C₂×Q₈⋊Dic₇	φ: C₂³.D₇/C₂×Dic₇ → C₂ ⊆ Aut C₄	448		C4.10(C2^3.D7)	448,758
C₄.₁₁(C₂³.D₇) = (Q₈×C₁₄)⋊₆C₄	φ: C₂³.D₇/C₂×Dic₇ → C₂ ⊆ Aut C₄	224		C4.11(C2^3.D7)	448,759
C₄.₁₂(C₂³.D₇) = C₂×C₂₈.₁₀D₄	φ: C₂³.D₇/C₂×Dic₇ → C₂ ⊆ Aut C₄	224		C4.12(C2^3.D7)	448,760
C₄.₁₃(C₂³.D₇) = (Q₈×C₁₄)⋊₇C₄	φ: C₂³.D₇/C₂×Dic₇ → C₂ ⊆ Aut C₄	448		C4.13(C2^3.D7)	448,764
C₄.₁₄(C₂³.D₇) = (D₄×C₁₄).₁₁C₄	φ: C₂³.D₇/C₂×Dic₇ → C₂ ⊆ Aut C₄	224		C4.14(C2^3.D7)	448,768
C₄.₁₅(C₂³.D₇) = C₂₈.₉C₄²	φ: C₂³.D₇/C₂²×C₁₄ → C₂ ⊆ Aut C₄	448		C4.15(C2^3.D7)	448,108
C₄.₁₆(C₂³.D₇) = C₂₈.₁₀C₄²	φ: C₂³.D₇/C₂²×C₁₄ → C₂ ⊆ Aut C₄	224		C4.16(C2^3.D7)	448,109
C₄.₁₇(C₂³.D₇) = M₄(2)⋊Dic₇	φ: C₂³.D₇/C₂²×C₁₄ → C₂ ⊆ Aut C₄	224		C4.17(C2^3.D7)	448,111
C₄.₁₈(C₂³.D₇) = C₂³.₉D₂₈	φ: C₂³.D₇/C₂²×C₁₄ → C₂ ⊆ Aut C₄	112	4	C4.18(C2^3.D7)	448,114
C₄.₁₉(C₂³.D₇) = M₄(2)⋊₄Dic₇	φ: C₂³.D₇/C₂²×C₁₄ → C₂ ⊆ Aut C₄	112	4	C4.19(C2^3.D7)	448,116
C₄.₂₀(C₂³.D₇) = C₂₈.₂₁C₄²	φ: C₂³.D₇/C₂²×C₁₄ → C₂ ⊆ Aut C₄	112	4	C4.20(C2^3.D7)	448,117
C₄.₂₁(C₂³.D₇) = C₂⁴.₄Dic₇	φ: C₂³.D₇/C₂²×C₁₄ → C₂ ⊆ Aut C₄	112		C4.21(C2^3.D7)	448,741
C₄.₂₂(C₂³.D₇) = C₄○D₄⋊Dic₇	φ: C₂³.D₇/C₂²×C₁₄ → C₂ ⊆ Aut C₄	224		C4.22(C2^3.D7)	448,766
C₄.₂₃(C₂³.D₇) = (D₄×C₁₄)⋊₉C₄	φ: C₂³.D₇/C₂²×C₁₄ → C₂ ⊆ Aut C₄	112	4	C4.23(C2^3.D7)	448,770
C₄.₂₄(C₂³.D₇) = C₅₆.₉₁D₄	central extension (φ=1)	224		C4.24(C2^3.D7)	448,106
C₄.₂₅(C₂³.D₇) = (C₂×C₅₆)⋊₅C₄	central extension (φ=1)	448		C4.25(C2^3.D7)	448,107
C₄.₂₆(C₂³.D₇) = C₅₆.D₄	central extension (φ=1)	112	4	C4.26(C2^3.D7)	448,110
C₄.₂₇(C₂³.D₇) = C₂₈.₃C₄²	central extension (φ=1)	112		C4.27(C2^3.D7)	448,112
C₄.₂₈(C₂³.D₇) = (C₂×C₅₆)⋊C₄	central extension (φ=1)	112	4	C4.28(C2^3.D7)	448,113
C₄.₂₉(C₂³.D₇) = C₂₈.₄C₄²	central extension (φ=1)	224		C4.29(C2^3.D7)	448,115
C₄.₃₀(C₂³.D₇) = C₅₆.₉₂D₄	central extension (φ=1)	224	4	C4.30(C2^3.D7)	448,118
C₄.₃₁(C₂³.D₇) = C₂×C₂₈.₅₅D₄	central extension (φ=1)	224		C4.31(C2^3.D7)	448,740
C₄.₃₂(C₂³.D₇) = C₂₈.(C₂×D₄)	central extension (φ=1)	224		C4.32(C2^3.D7)	448,767
C₄.₃₃(C₂³.D₇) = C₂×D₄⋊₂Dic₇	central extension (φ=1)	112		C4.33(C2^3.D7)	448,769
C₄.₃₄(C₂³.D₇) = (D₄×C₁₄).₁₆C₄	central extension (φ=1)	112	4	C4.34(C2^3.D7)	448,771
C₄.₃₅(C₂³.D₇) = (D₄×C₁₄)⋊₁₀C₄	central extension (φ=1)	112	4	C4.35(C2^3.D7)	448,774

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C4 and Q=C23.D7

Extensions 1→N→G→Q→1 with N=C₄ and Q=C₂³.D₇