Extensions 1→N→G→Q→1 with N=C₁₂ and Q=S₃

Direct product G=N×Q with N=C₁₂ and Q=S₃

		d	ρ	Label	ID
S₃×C₁₂		24	2	S3xC12	72,27

Semidirect products G=N:Q with N=C₁₂ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₂⋊₁S₃ = C₁₂⋊S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₁₂	36		C12:1S3	72,33
C₁₂⋊₂S₃ = C₄×C₃⋊S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₁₂	36		C12:2S3	72,32
C₁₂⋊₃S₃ = C₃×D₁₂	φ: S₃/C₃ → C₂ ⊆ Aut C₁₂	24	2	C12:3S3	72,28

Non-split extensions G=N.Q with N=C₁₂ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₂.₁S₃ = Dic₁₈	φ: S₃/C₃ → C₂ ⊆ Aut C₁₂	72	2-	C12.1S3	72,4
C₁₂.₂S₃ = D₃₆	φ: S₃/C₃ → C₂ ⊆ Aut C₁₂	36	2+	C12.2S3	72,6
C₁₂.₃S₃ = C₃²⋊₄Q₈	φ: S₃/C₃ → C₂ ⊆ Aut C₁₂	72		C12.3S3	72,31
C₁₂.₄S₃ = C₉⋊C₈	φ: S₃/C₃ → C₂ ⊆ Aut C₁₂	72	2	C12.4S3	72,1
C₁₂.₅S₃ = C₄×D₉	φ: S₃/C₃ → C₂ ⊆ Aut C₁₂	36	2	C12.5S3	72,5
C₁₂.₆S₃ = C₃²⋊₄C₈	φ: S₃/C₃ → C₂ ⊆ Aut C₁₂	72		C12.6S3	72,13
C₁₂.₇S₃ = C₃×Dic₆	φ: S₃/C₃ → C₂ ⊆ Aut C₁₂	24	2	C12.7S3	72,26
C₁₂.₈S₃ = C₃×C₃⋊C₈	central extension (φ=1)	24	2	C12.8S3	72,12

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