Extensions 1→N→G→Q→1 with N=C₃ and Q=C₃×D₄⋊S₃

Direct product G=N×Q with N=C₃ and Q=C₃×D₄⋊S₃

		d	ρ	Label	ID
C₃²×D₄⋊S₃		72		C3^2xD4:S3	432,475

Semidirect products G=N:Q with N=C₃ and Q=C₃×D₄⋊S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(C₃×D₄⋊S₃) = C₃×C₃⋊D₂₄	φ: C₃×D₄⋊S₃/C₃×C₃⋊C₈ → C₂ ⊆ Aut C₃	48	4	C3:1(C3xD4:S3)	432,419
C₃⋊₂(C₃×D₄⋊S₃) = C₃×C₃²⋊₂D₈	φ: C₃×D₄⋊S₃/C₃×D₁₂ → C₂ ⊆ Aut C₃	48	4	C3:2(C3xD4:S3)	432,418
C₃⋊₃(C₃×D₄⋊S₃) = C₃×C₃²⋊₇D₈	φ: C₃×D₄⋊S₃/D₄×C₃² → C₂ ⊆ Aut C₃	72		C3:3(C3xD4:S3)	432,491

Non-split extensions G=N.Q with N=C₃ and Q=C₃×D₄⋊S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₃×D₄⋊S₃) = C₃×D₄⋊D₉	φ: C₃×D₄⋊S₃/D₄×C₃² → C₂ ⊆ Aut C₃	72	4	C3.1(C3xD4:S3)	432,149
C₃.₂(C₃×D₄⋊S₃) = He₃⋊₆D₈	φ: C₃×D₄⋊S₃/D₄×C₃² → C₂ ⊆ Aut C₃	72	12+	C3.2(C3xD4:S3)	432,153
C₃.₃(C₃×D₄⋊S₃) = D₃₆⋊C₆	φ: C₃×D₄⋊S₃/D₄×C₃² → C₂ ⊆ Aut C₃	72	12+	C3.3(C3xD4:S3)	432,155
C₃.₄(C₃×D₄⋊S₃) = C₉×D₄⋊S₃	central extension (φ=1)	72	4	C3.4(C3xD4:S3)	432,150

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