Extensions 1→N→G→Q→1 with N=C₃ and Q=D₁₂⋊₆C₂²

Direct product G=N×Q with N=C₃ and Q=D₁₂⋊₆C₂²

		d	ρ	Label	ID
C₃×D₁₂⋊₆C₂²		24	4	C3xD12:6C2^2	288,703

Semidirect products G=N:Q with N=C₃ and Q=D₁₂⋊₆C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(D₁₂⋊₆C₂²) = D₁₂.₂₈D₆	φ: D₁₂⋊₆C₂²/C₄.Dic₃ → C₂ ⊆ Aut C₃	48	4	C3:1(D12:6C2^2)	288,478
C₃⋊₂(D₁₂⋊₆C₂²) = D₁₂⋊₉D₆	φ: D₁₂⋊₆C₂²/D₄⋊S₃ → C₂ ⊆ Aut C₃	48	8-	C3:2(D12:6C2^2)	288,580
C₃⋊₃(D₁₂⋊₆C₂²) = D₁₂.₇D₆	φ: D₁₂⋊₆C₂²/D₄.S₃ → C₂ ⊆ Aut C₃	48	8+	C3:3(D12:6C2^2)	288,582
C₃⋊₄(D₁₂⋊₆C₂²) = D₁₂⋊₂₀D₆	φ: D₁₂⋊₆C₂²/C₄○D₁₂ → C₂ ⊆ Aut C₃	48	4	C3:4(D12:6C2^2)	288,471
C₃⋊₅(D₁₂⋊₆C₂²) = C₆².₁₃₁D₄	φ: D₁₂⋊₆C₂²/C₆×D₄ → C₂ ⊆ Aut C₃	72		C3:5(D12:6C2^2)	288,789

Non-split extensions G=N.Q with N=C₃ and Q=D₁₂⋊₆C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(D₁₂⋊₆C₂²) = D₃₆⋊₆C₂²	φ: D₁₂⋊₆C₂²/C₆×D₄ → C₂ ⊆ Aut C₃	72	4	C3.(D12:6C2^2)	288,143

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