Extensions 1→N→G→Q→1 with N=C₁₂ and Q=D₇

Direct product G=N×Q with N=C₁₂ and Q=D₇

		d	ρ	Label	ID
C₁₂×D₇		84	2	C12xD7	168,25

Semidirect products G=N:Q with N=C₁₂ and Q=D₇

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₂⋊₁D₇ = D₈₄	φ: D₇/C₇ → C₂ ⊆ Aut C₁₂	84	2+	C12:1D7	168,36
C₁₂⋊₂D₇ = C₄×D₂₁	φ: D₇/C₇ → C₂ ⊆ Aut C₁₂	84	2	C12:2D7	168,35
C₁₂⋊₃D₇ = C₃×D₂₈	φ: D₇/C₇ → C₂ ⊆ Aut C₁₂	84	2	C12:3D7	168,26

Non-split extensions G=N.Q with N=C₁₂ and Q=D₇

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₂.₁D₇ = Dic₄₂	φ: D₇/C₇ → C₂ ⊆ Aut C₁₂	168	2-	C12.1D7	168,34
C₁₂.₂D₇ = C₂₁⋊C₈	φ: D₇/C₇ → C₂ ⊆ Aut C₁₂	168	2	C12.2D7	168,5
C₁₂.₃D₇ = C₃×Dic₁₄	φ: D₇/C₇ → C₂ ⊆ Aut C₁₂	168	2	C12.3D7	168,24
C₁₂.₄D₇ = C₃×C₇⋊C₈	central extension (φ=1)	168	2	C12.4D7	168,4

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