Extensions 1→N→G→Q→1 with N=C₃ and Q=C₁₂.₂₃D₄

Direct product G=N×Q with N=C₃ and Q=C₁₂.₂₃D₄

		d	ρ	Label	ID
C₃×C₁₂.₂₃D₄		96		C3xC12.23D4	288,718

Semidirect products G=N:Q with N=C₃ and Q=C₁₂.₂₃D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(C₁₂.₂₃D₄) = C₁₂.₂₈D₁₂	φ: C₁₂.₂₃D₄/C₄×Dic₃ → C₂ ⊆ Aut C₃	48		C3:1(C12.23D4)	288,512
C₃⋊₂(C₁₂.₂₃D₄) = C₆².₇₇C₂³	φ: C₁₂.₂₃D₄/D₆⋊C₄ → C₂ ⊆ Aut C₃	48		C3:2(C12.23D4)	288,555
C₃⋊₃(C₁₂.₂₃D₄) = C₆².₃₃C₂³	φ: C₁₂.₂₃D₄/C₂×D₁₂ → C₂ ⊆ Aut C₃	96		C3:3(C12.23D4)	288,511
C₃⋊₄(C₁₂.₂₃D₄) = C₆².₂₆₂C₂³	φ: C₁₂.₂₃D₄/C₆×Q₈ → C₂ ⊆ Aut C₃	144		C3:4(C12.23D4)	288,804

Non-split extensions G=N.Q with N=C₃ and Q=C₁₂.₂₃D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(C₁₂.₂₃D₄) = C₃₆.₂₃D₄	φ: C₁₂.₂₃D₄/C₆×Q₈ → C₂ ⊆ Aut C₃	144		C3.(C12.23D4)	288,157

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