Extensions 1→N→G→Q→1 with N=C₂² and Q=C₂×F₇

Direct product G=N×Q with N=C₂² and Q=C₂×F₇

		d	ρ	Label	ID
C₂³×F₇		56		C2^3xF7	336,216

Semidirect products G=N:Q with N=C₂² and Q=C₂×F₇

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂²⋊(C₂×F₇) = C₂×D₇⋊A₄	φ: C₂×F₇/D₁₄ → C₃ ⊆ Aut C₂²	42	6+	C2^2:(C2xF7)	336,218
C₂²⋊₂(C₂×F₇) = D₄×F₇	φ: C₂×F₇/F₇ → C₂ ⊆ Aut C₂²	28	12+	C2^2:2(C2xF7)	336,125
C₂²⋊₃(C₂×F₇) = C₂×Dic₇⋊C₆	φ: C₂×F₇/C₂×C₇⋊C₃ → C₂ ⊆ Aut C₂²	56		C2^2:3(C2xF7)	336,130

Non-split extensions G=N.Q with N=C₂² and Q=C₂×F₇

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂².₁(C₂×F₇) = D₄⋊₂F₇	φ: C₂×F₇/F₇ → C₂ ⊆ Aut C₂²	56	12-	C2^2.1(C2xF7)	336,126
C₂².₂(C₂×F₇) = D₂₈⋊₆C₆	φ: C₂×F₇/C₂×C₇⋊C₃ → C₂ ⊆ Aut C₂²	56	6	C2^2.2(C2xF7)	336,124
C₂².₃(C₂×F₇) = C₄×C₇⋊C₁₂	central extension (φ=1)	112		C2^2.3(C2xF7)	336,14
C₂².₄(C₂×F₇) = Dic₇⋊C₁₂	central extension (φ=1)	112		C2^2.4(C2xF7)	336,15
C₂².₅(C₂×F₇) = C₂₈⋊C₁₂	central extension (φ=1)	112		C2^2.5(C2xF7)	336,16
C₂².₆(C₂×F₇) = D₁₄⋊C₁₂	central extension (φ=1)	56		C2^2.6(C2xF7)	336,17
C₂².₇(C₂×F₇) = C₂³.₂F₇	central extension (φ=1)	56		C2^2.7(C2xF7)	336,22
C₂².₈(C₂×F₇) = C₂×C₄.F₇	central extension (φ=1)	112		C2^2.8(C2xF7)	336,121
C₂².₉(C₂×F₇) = C₂×C₄×F₇	central extension (φ=1)	56		C2^2.9(C2xF7)	336,122
C₂².₁₀(C₂×F₇) = C₂×C₄⋊F₇	central extension (φ=1)	56		C2^2.10(C2xF7)	336,123
C₂².₁₁(C₂×F₇) = C₂²×C₇⋊C₁₂	central extension (φ=1)	112		C2^2.11(C2xF7)	336,129

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