Extensions 1→N→G→Q→1 with N=C₃ and Q=C₄⋊C₄⋊₇S₃

Direct product G=N×Q with N=C₃ and Q=C₄⋊C₄⋊₇S₃

		d	ρ	Label	ID
C₃×C₄⋊C₄⋊₇S₃		96		C3xC4:C4:7S3	288,663

Semidirect products G=N:Q with N=C₃ and Q=C₄⋊C₄⋊₇S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(C₄⋊C₄⋊₇S₃) = C₆².₆C₂³	φ: C₄⋊C₄⋊₇S₃/C₄×Dic₃ → C₂ ⊆ Aut C₃	48		C3:1(C4:C4:7S3)	288,484
C₃⋊₂(C₄⋊C₄⋊₇S₃) = C₆².₁₉C₂³	φ: C₄⋊C₄⋊₇S₃/C₄⋊Dic₃ → C₂ ⊆ Aut C₃	48		C3:2(C4:C4:7S3)	288,497
C₃⋊₃(C₄⋊C₄⋊₇S₃) = C₆².₄₈C₂³	φ: C₄⋊C₄⋊₇S₃/D₆⋊C₄ → C₂ ⊆ Aut C₃	96		C3:3(C4:C4:7S3)	288,526
C₃⋊₄(C₄⋊C₄⋊₇S₃) = C₆².₂₃₆C₂³	φ: C₄⋊C₄⋊₇S₃/C₃×C₄⋊C₄ → C₂ ⊆ Aut C₃	144		C3:4(C4:C4:7S3)	288,749
C₃⋊₅(C₄⋊C₄⋊₇S₃) = C₆².₁₁C₂³	φ: C₄⋊C₄⋊₇S₃/S₃×C₂×C₄ → C₂ ⊆ Aut C₃	96		C3:5(C4:C4:7S3)	288,489

Non-split extensions G=N.Q with N=C₃ and Q=C₄⋊C₄⋊₇S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(C₄⋊C₄⋊₇S₃) = C₄⋊C₄⋊₇D₉	φ: C₄⋊C₄⋊₇S₃/C₃×C₄⋊C₄ → C₂ ⊆ Aut C₃	144		C3.(C4:C4:7S3)	288,102

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