Extensions 1→N→G→Q→1 with N=C₁₂ and Q=C₄

Direct product G=N×Q with N=C₁₂ and Q=C₄

		d	ρ	Label	ID
C₄×C₁₂		48		C4xC12	48,20

Semidirect products G=N:Q with N=C₁₂ and Q=C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₂⋊₁C₄ = C₄⋊Dic₃	φ: C₄/C₂ → C₂ ⊆ Aut C₁₂	48		C12:1C4	48,13
C₁₂⋊₂C₄ = C₄×Dic₃	φ: C₄/C₂ → C₂ ⊆ Aut C₁₂	48		C12:2C4	48,11
C₁₂⋊₃C₄ = C₃×C₄⋊C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₁₂	48		C12:3C4	48,22

Non-split extensions G=N.Q with N=C₁₂ and Q=C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₂.₁C₄ = C₄.Dic₃	φ: C₄/C₂ → C₂ ⊆ Aut C₁₂	24	2	C12.1C4	48,10
C₁₂.₂C₄ = C₃⋊C₁₆	φ: C₄/C₂ → C₂ ⊆ Aut C₁₂	48	2	C12.2C4	48,1
C₁₂.₃C₄ = C₂×C₃⋊C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₁₂	48		C12.3C4	48,9
C₁₂.₄C₄ = C₃×M₄(2)	φ: C₄/C₂ → C₂ ⊆ Aut C₁₂	24	2	C12.4C4	48,24

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