Extensions 1→N→G→Q→1 with N=C₄ and Q=C₂×F₇

Direct product G=N×Q with N=C₄ and Q=C₂×F₇

		d	ρ	Label	ID
C₂×C₄×F₇		56		C2xC4xF7	336,122

Semidirect products G=N:Q with N=C₄ and Q=C₂×F₇

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊₁(C₂×F₇) = D₄×F₇	φ: C₂×F₇/F₇ → C₂ ⊆ Aut C₄	28	12+	C4:1(C2xF7)	336,125
C₄⋊₂(C₂×F₇) = C₂×C₄⋊F₇	φ: C₂×F₇/C₂×C₇⋊C₃ → C₂ ⊆ Aut C₄	56		C4:2(C2xF7)	336,123

Non-split extensions G=N.Q with N=C₄ and Q=C₂×F₇

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁(C₂×F₇) = D₄⋊F₇	φ: C₂×F₇/F₇ → C₂ ⊆ Aut C₄	56	12+	C4.1(C2xF7)	336,18
C₄.₂(C₂×F₇) = D₄.F₇	φ: C₂×F₇/F₇ → C₂ ⊆ Aut C₄	56	12-	C4.2(C2xF7)	336,19
C₄.₃(C₂×F₇) = Q₈⋊₂F₇	φ: C₂×F₇/F₇ → C₂ ⊆ Aut C₄	56	12+	C4.3(C2xF7)	336,20
C₄.₄(C₂×F₇) = Q₈.₂F₇	φ: C₂×F₇/F₇ → C₂ ⊆ Aut C₄	112	12-	C4.4(C2xF7)	336,21
C₄.₅(C₂×F₇) = D₄⋊₂F₇	φ: C₂×F₇/F₇ → C₂ ⊆ Aut C₄	56	12-	C4.5(C2xF7)	336,126
C₄.₆(C₂×F₇) = Q₈×F₇	φ: C₂×F₇/F₇ → C₂ ⊆ Aut C₄	56	12-	C4.6(C2xF7)	336,127
C₄.₇(C₂×F₇) = Q₈⋊₃F₇	φ: C₂×F₇/F₇ → C₂ ⊆ Aut C₄	56	12+	C4.7(C2xF7)	336,128
C₄.₈(C₂×F₇) = C₅₆⋊C₆	φ: C₂×F₇/C₂×C₇⋊C₃ → C₂ ⊆ Aut C₄	56	6	C4.8(C2xF7)	336,9
C₄.₉(C₂×F₇) = D₅₆⋊C₃	φ: C₂×F₇/C₂×C₇⋊C₃ → C₂ ⊆ Aut C₄	56	6+	C4.9(C2xF7)	336,10
C₄.₁₀(C₂×F₇) = C₈.F₇	φ: C₂×F₇/C₂×C₇⋊C₃ → C₂ ⊆ Aut C₄	112	6-	C4.10(C2xF7)	336,11
C₄.₁₁(C₂×F₇) = C₂×C₄.F₇	φ: C₂×F₇/C₂×C₇⋊C₃ → C₂ ⊆ Aut C₄	112		C4.11(C2xF7)	336,121
C₄.₁₂(C₂×F₇) = C₈×F₇	central extension (φ=1)	56	6	C4.12(C2xF7)	336,7
C₄.₁₃(C₂×F₇) = C₈⋊F₇	central extension (φ=1)	56	6	C4.13(C2xF7)	336,8
C₄.₁₄(C₂×F₇) = C₂×C₇⋊C₂₄	central extension (φ=1)	112		C4.14(C2xF7)	336,12
C₄.₁₅(C₂×F₇) = C₂₈.C₁₂	central extension (φ=1)	56	6	C4.15(C2xF7)	336,13
C₄.₁₆(C₂×F₇) = D₂₈⋊₆C₆	central extension (φ=1)	56	6	C4.16(C2xF7)	336,124

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