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

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

		d	ρ	Label	ID
C₃×C₄⋊C₄⋊S₃		96		C3xC4:C4:S3	288,669

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(C₄⋊C₄⋊S₃) = C₆².₃₈C₂³	φ: C₄⋊C₄⋊S₃/C₄×Dic₃ → C₂ ⊆ Aut C₃	48		C3:1(C4:C4:S3)	288,516
C₃⋊₂(C₄⋊C₄⋊S₃) = C₆².₁₈C₂³	φ: C₄⋊C₄⋊S₃/C₄⋊Dic₃ → C₂ ⊆ Aut C₃	48		C3:2(C4:C4:S3)	288,496
C₃⋊₃(C₄⋊C₄⋊S₃) = C₆².₂₈C₂³	φ: C₄⋊C₄⋊S₃/D₆⋊C₄ → C₂ ⊆ Aut C₃	96		C3:3(C4:C4:S3)	288,506
C₃⋊₄(C₄⋊C₄⋊S₃) = C₆².₃₁C₂³	φ: C₄⋊C₄⋊S₃/D₆⋊C₄ → C₂ ⊆ Aut C₃	96		C3:4(C4:C4:S3)	288,509
C₃⋊₅(C₄⋊C₄⋊S₃) = C₆².₃₂C₂³	φ: C₄⋊C₄⋊S₃/D₆⋊C₄ → C₂ ⊆ Aut C₃	96		C3:5(C4:C4:S3)	288,510
C₃⋊₆(C₄⋊C₄⋊S₃) = C₆².₂₄₂C₂³	φ: C₄⋊C₄⋊S₃/C₃×C₄⋊C₄ → C₂ ⊆ Aut C₃	144		C3:6(C4:C4:S3)	288,755

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(C₄⋊C₄⋊S₃) = C₄⋊C₄⋊D₉	φ: C₄⋊C₄⋊S₃/C₃×C₄⋊C₄ → C₂ ⊆ Aut C₃	144		C3.(C4:C4:S3)	288,108

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