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

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

		d	ρ	Label	ID
C₃⋊S₃×D₁₂		72		C3:S3xD12	432,672

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

extension	φ:Q→Out N	d	ρ	Label	ID
D₁₂⋊₁(C₃⋊S₃) = C₃³⋊₇D₈	φ: C₃⋊S₃/C₃² → C₂ ⊆ Out D₁₂	72		D12:1(C3:S3)	432,437
D₁₂⋊₂(C₃⋊S₃) = C₃³⋊₆D₈	φ: C₃⋊S₃/C₃² → C₂ ⊆ Out D₁₂	144		D12:2(C3:S3)	432,436
D₁₂⋊₃(C₃⋊S₃) = D₁₂⋊(C₃⋊S₃)	φ: C₃⋊S₃/C₃² → C₂ ⊆ Out D₁₂	72		D12:3(C3:S3)	432,662
D₁₂⋊₄(C₃⋊S₃) = C₁₂⋊S₃²	φ: C₃⋊S₃/C₃² → C₂ ⊆ Out D₁₂	72		D12:4(C3:S3)	432,673
D₁₂⋊₅(C₃⋊S₃) = (C₃×D₁₂)⋊S₃	φ: trivial image	144		D12:5(C3:S3)	432,661

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

extension	φ:Q→Out N	d	ρ	Label	ID
D₁₂.₁(C₃⋊S₃) = C₃³⋊₁₄SD₁₆	φ: C₃⋊S₃/C₃² → C₂ ⊆ Out D₁₂	144		D12.1(C3:S3)	432,441
D₁₂.₂(C₃⋊S₃) = C₃³⋊₁₂SD₁₆	φ: C₃⋊S₃/C₃² → C₂ ⊆ Out D₁₂	144		D12.2(C3:S3)	432,439

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁