Extensions 1→N→G→Q→1 with N=C₂³ and Q=C₃.A₄

Direct product G=N×Q with N=C₂³ and Q=C₃.A₄

		d	ρ	Label	ID
C₂³×C₃.A₄		72		C2^3xC3.A4	288,837

Semidirect products G=N:Q with N=C₂³ and Q=C₃.A₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³⋊₁(C₃.A₄) = C₂⁴⋊C₁₈	φ: C₃.A₄/C₃ → A₄ ⊆ Aut C₂³	36	6	C2^3:1(C3.A4)	288,73
C₂³⋊₂(C₃.A₄) = 2₊¹⁺⁴⋊₂C₉	φ: C₃.A₄/C₃ → A₄ ⊆ Aut C₂³	72	4	C2^3:2(C3.A4)	288,351
C₂³⋊₃(C₃.A₄) = C₂×C₂⁴⋊C₉	φ: C₃.A₄/C₂×C₆ → C₃ ⊆ Aut C₂³	36		C2^3:3(C3.A4)	288,838

Non-split extensions G=N.Q with N=C₂³ and Q=C₃.A₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³.₁(C₃.A₄) = C₄²⋊C₁₈	φ: C₃.A₄/C₃ → A₄ ⊆ Aut C₂³	72	6	C2^3.1(C3.A4)	288,74
C₂³.₂(C₃.A₄) = C₄²⋊₂C₁₈	φ: C₃.A₄/C₃ → A₄ ⊆ Aut C₂³	36	6	C2^3.2(C3.A4)	288,75
C₂³.₃(C₃.A₄) = C₂.(C₄²⋊C₉)	φ: C₃.A₄/C₂×C₆ → C₃ ⊆ Aut C₂³	36	6	C2^3.3(C3.A4)	288,3
C₂³.₄(C₃.A₄) = C₂×C₄²⋊C₉	φ: C₃.A₄/C₂×C₆ → C₃ ⊆ Aut C₂³	36	3	C2^3.4(C3.A4)	288,71
C₂³.₅(C₃.A₄) = C₂²⋊(Q₈⋊C₉)	φ: C₃.A₄/C₂×C₆ → C₃ ⊆ Aut C₂³	72	6	C2^3.5(C3.A4)	288,350
C₂³.₆(C₃.A₄) = C₂²×Q₈⋊C₉	central extension (φ=1)	288		C2^3.6(C3.A4)	288,345

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