Extensions 1→N→G→Q→1 with N=C₃×C₁₂ and Q=C₂

Direct product G=N×Q with N=C₃×C₁₂ and Q=C₂

		d	ρ	Label	ID
C₆×C₁₂		72		C6xC12	72,36

Semidirect products G=N:Q with N=C₃×C₁₂ and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃×C₁₂)⋊₁C₂ = C₁₂⋊S₃	φ: C₂/C₁ → C₂ ⊆ Aut C₃×C₁₂	36		(C3xC12):1C2	72,33
(C₃×C₁₂)⋊₂C₂ = C₃×D₁₂	φ: C₂/C₁ → C₂ ⊆ Aut C₃×C₁₂	24	2	(C3xC12):2C2	72,28
(C₃×C₁₂)⋊₃C₂ = S₃×C₁₂	φ: C₂/C₁ → C₂ ⊆ Aut C₃×C₁₂	24	2	(C3xC12):3C2	72,27
(C₃×C₁₂)⋊₄C₂ = C₄×C₃⋊S₃	φ: C₂/C₁ → C₂ ⊆ Aut C₃×C₁₂	36		(C3xC12):4C2	72,32
(C₃×C₁₂)⋊₅C₂ = D₄×C₃²	φ: C₂/C₁ → C₂ ⊆ Aut C₃×C₁₂	36		(C3xC12):5C2	72,37

Non-split extensions G=N.Q with N=C₃×C₁₂ and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃×C₁₂).₁C₂ = C₃²⋊₄Q₈	φ: C₂/C₁ → C₂ ⊆ Aut C₃×C₁₂	72		(C3xC12).1C2	72,31
(C₃×C₁₂).₂C₂ = C₃×Dic₆	φ: C₂/C₁ → C₂ ⊆ Aut C₃×C₁₂	24	2	(C3xC12).2C2	72,26
(C₃×C₁₂).₃C₂ = C₃×C₃⋊C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₃×C₁₂	24	2	(C3xC12).3C2	72,12
(C₃×C₁₂).₄C₂ = C₃²⋊₄C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₃×C₁₂	72		(C3xC12).4C2	72,13
(C₃×C₁₂).₅C₂ = Q₈×C₃²	φ: C₂/C₁ → C₂ ⊆ Aut C₃×C₁₂	72		(C3xC12).5C2	72,38

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁