Extensions 1→N→G→Q→1 with N=C₆ and Q=C₇×D₄

Direct product G=N×Q with N=C₆ and Q=C₇×D₄

		d	ρ	Label	ID
D₄×C₄₂		168		D4xC42	336,205

Semidirect products G=N:Q with N=C₆ and Q=C₇×D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆⋊₁(C₇×D₄) = C₁₄×D₁₂	φ: C₇×D₄/C₂₈ → C₂ ⊆ Aut C₆	168		C6:1(C7xD4)	336,186
C₆⋊₂(C₇×D₄) = C₁₄×C₃⋊D₄	φ: C₇×D₄/C₂×C₁₄ → C₂ ⊆ Aut C₆	168		C6:2(C7xD4)	336,193

Non-split extensions G=N.Q with N=C₆ and Q=C₇×D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆.₁(C₇×D₄) = C₇×C₂₄⋊C₂	φ: C₇×D₄/C₂₈ → C₂ ⊆ Aut C₆	168	2	C6.1(C7xD4)	336,76
C₆.₂(C₇×D₄) = C₇×D₂₄	φ: C₇×D₄/C₂₈ → C₂ ⊆ Aut C₆	168	2	C6.2(C7xD4)	336,77
C₆.₃(C₇×D₄) = C₇×Dic₁₂	φ: C₇×D₄/C₂₈ → C₂ ⊆ Aut C₆	336	2	C6.3(C7xD4)	336,78
C₆.₄(C₇×D₄) = C₇×C₄⋊Dic₃	φ: C₇×D₄/C₂₈ → C₂ ⊆ Aut C₆	336		C6.4(C7xD4)	336,83
C₆.₅(C₇×D₄) = C₇×Dic₃⋊C₄	φ: C₇×D₄/C₂×C₁₄ → C₂ ⊆ Aut C₆	336		C6.5(C7xD4)	336,82
C₆.₆(C₇×D₄) = C₇×D₆⋊C₄	φ: C₇×D₄/C₂×C₁₄ → C₂ ⊆ Aut C₆	168		C6.6(C7xD4)	336,84
C₆.₇(C₇×D₄) = C₇×D₄⋊S₃	φ: C₇×D₄/C₂×C₁₄ → C₂ ⊆ Aut C₆	168	4	C6.7(C7xD4)	336,85
C₆.₈(C₇×D₄) = C₇×D₄.S₃	φ: C₇×D₄/C₂×C₁₄ → C₂ ⊆ Aut C₆	168	4	C6.8(C7xD4)	336,86
C₆.₉(C₇×D₄) = C₇×Q₈⋊₂S₃	φ: C₇×D₄/C₂×C₁₄ → C₂ ⊆ Aut C₆	168	4	C6.9(C7xD4)	336,87
C₆.₁₀(C₇×D₄) = C₇×C₃⋊Q₁₆	φ: C₇×D₄/C₂×C₁₄ → C₂ ⊆ Aut C₆	336	4	C6.10(C7xD4)	336,88
C₆.₁₁(C₇×D₄) = C₇×C₆.D₄	φ: C₇×D₄/C₂×C₁₄ → C₂ ⊆ Aut C₆	168		C6.11(C7xD4)	336,89
C₆.₁₂(C₇×D₄) = C₂²⋊C₄×C₂₁	central extension (φ=1)	168		C6.12(C7xD4)	336,107
C₆.₁₃(C₇×D₄) = C₄⋊C₄×C₂₁	central extension (φ=1)	336		C6.13(C7xD4)	336,108
C₆.₁₄(C₇×D₄) = D₈×C₂₁	central extension (φ=1)	168	2	C6.14(C7xD4)	336,111
C₆.₁₅(C₇×D₄) = SD₁₆×C₂₁	central extension (φ=1)	168	2	C6.15(C7xD4)	336,112
C₆.₁₆(C₇×D₄) = Q₁₆×C₂₁	central extension (φ=1)	336	2	C6.16(C7xD4)	336,113

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