Extensions 1→N→G→Q→1 with N=C₃ and Q=D₁₂⋊₅S₃

Direct product G=N×Q with N=C₃ and Q=D₁₂⋊₅S₃

		d	ρ	Label	ID
C₃×D₁₂⋊₅S₃		48	4	C3xD12:5S3	432,643

Semidirect products G=N:Q with N=C₃ and Q=D₁₂⋊₅S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(D₁₂⋊₅S₃) = D₆.S₃²	φ: D₁₂⋊₅S₃/S₃×Dic₃ → C₂ ⊆ Aut C₃	48	8-	C3:1(D12:5S3)	432,607
C₃⋊₂(D₁₂⋊₅S₃) = D₆.₄S₃²	φ: D₁₂⋊₅S₃/D₆⋊S₃ → C₂ ⊆ Aut C₃	48	8-	C3:2(D12:5S3)	432,608
C₃⋊₃(D₁₂⋊₅S₃) = C₁₂.₅₇S₃²	φ: D₁₂⋊₅S₃/S₃×C₁₂ → C₂ ⊆ Aut C₃	144		C3:3(D12:5S3)	432,668
C₃⋊₄(D₁₂⋊₅S₃) = (C₃×D₁₂)⋊S₃	φ: D₁₂⋊₅S₃/C₃×D₁₂ → C₂ ⊆ Aut C₃	144		C3:4(D12:5S3)	432,661
C₃⋊₅(D₁₂⋊₅S₃) = C₁₂⋊S₃⋊₁₂S₃	φ: D₁₂⋊₅S₃/C₃²⋊₄Q₈ → C₂ ⊆ Aut C₃	48	4	C3:5(D12:5S3)	432,688

Non-split extensions G=N.Q with N=C₃ and Q=D₁₂⋊₅S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(D₁₂⋊₅S₃) = D₃₆⋊₅S₃	φ: D₁₂⋊₅S₃/S₃×C₁₂ → C₂ ⊆ Aut C₃	144	4-	C3.1(D12:5S3)	432,288
C₃.₂(D₁₂⋊₅S₃) = D₁₂⋊₅D₉	φ: D₁₂⋊₅S₃/C₃×D₁₂ → C₂ ⊆ Aut C₃	144	4-	C3.2(D12:5S3)	432,285
C₃.₃(D₁₂⋊₅S₃) = C₁₂⋊S₃⋊S₃	φ: D₁₂⋊₅S₃/C₃²⋊₄Q₈ → C₂ ⊆ Aut C₃	72	12+	C3.3(D12:5S3)	432,295

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