Extensions 1→N→G→Q→1 with N=C₃ and Q=C₁₂.D₆

Direct product G=N×Q with N=C₃ and Q=C₁₂.D₆

		d	ρ	Label	ID
C₃×C₁₂.D₆		72		C3xC12.D6	432,715

Semidirect products G=N:Q with N=C₃ and Q=C₁₂.D₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(C₁₂.D₆) = D₁₂⋊(C₃⋊S₃)	φ: C₁₂.D₆/C₃²⋊₄Q₈ → C₂ ⊆ Aut C₃	72		C3:1(C12.D6)	432,662
C₃⋊₂(C₁₂.D₆) = (C₃×D₁₂)⋊S₃	φ: C₁₂.D₆/C₄×C₃⋊S₃ → C₂ ⊆ Aut C₃	144		C3:2(C12.D6)	432,661
C₃⋊₃(C₁₂.D₆) = C₆².₉₀D₆	φ: C₁₂.D₆/C₂×C₃⋊Dic₃ → C₂ ⊆ Aut C₃	72		C3:3(C12.D6)	432,675
C₃⋊₄(C₁₂.D₆) = C₆².₉₁D₆	φ: C₁₂.D₆/C₃²⋊₇D₄ → C₂ ⊆ Aut C₃	72		C3:4(C12.D6)	432,676
C₃⋊₅(C₁₂.D₆) = C₆².₁₀₀D₆	φ: C₁₂.D₆/D₄×C₃² → C₂ ⊆ Aut C₃	216		C3:5(C12.D6)	432,725

Non-split extensions G=N.Q with N=C₃ and Q=C₁₂.D₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(C₁₂.D₆) = C₃₆.₂₇D₆	φ: C₁₂.D₆/D₄×C₃² → C₂ ⊆ Aut C₃	216		C3.(C12.D6)	432,389
C₃.₂(C₁₂.D₆) = C₆².₁₆D₆	central stem extension (φ=1)	72	6	C3.2(C12.D6)	432,391

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