Extensions 1→N→G→Q→1 with N=C₃ and Q=C₄²⋊₇S₃

Direct product G=N×Q with N=C₃ and Q=C₄²⋊₇S₃

		d	ρ	Label	ID
C₃×C₄²⋊₇S₃		96		C3xC4^2:7S3	288,646

Semidirect products G=N:Q with N=C₃ and Q=C₄²⋊₇S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(C₄²⋊₇S₃) = Dic₃.D₁₂	φ: C₄²⋊₇S₃/D₆⋊C₄ → C₂ ⊆ Aut C₃	48		C3:1(C4^2:7S3)	288,500
C₃⋊₂(C₄²⋊₇S₃) = C₁₂²⋊₆C₂	φ: C₄²⋊₇S₃/C₄×C₁₂ → C₂ ⊆ Aut C₃	144		C3:2(C4^2:7S3)	288,732
C₃⋊₃(C₄²⋊₇S₃) = C₁₂.₂₈D₁₂	φ: C₄²⋊₇S₃/C₂×Dic₆ → C₂ ⊆ Aut C₃	48		C3:3(C4^2:7S3)	288,512
C₃⋊₄(C₄²⋊₇S₃) = C₁₂.₂₇D₁₂	φ: C₄²⋊₇S₃/C₂×D₁₂ → C₂ ⊆ Aut C₃	96		C3:4(C4^2:7S3)	288,508

Non-split extensions G=N.Q with N=C₃ and Q=C₄²⋊₇S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(C₄²⋊₇S₃) = C₄²⋊₇D₉	φ: C₄²⋊₇S₃/C₄×C₁₂ → C₂ ⊆ Aut C₃	144		C3.(C4^2:7S3)	288,85

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