Extensions 1→N→G→Q→1 with N=C₂⁴ and Q=C₃×C₆

Direct product G=N×Q with N=C₂⁴ and Q=C₃×C₆

		d	ρ	Label	ID
C₂³×C₆²		288		C2^3xC6^2	288,1045

Semidirect products G=N:Q with N=C₂⁴ and Q=C₃×C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂⁴⋊(C₃×C₆) = C₂×A₄²	φ: C₃×C₆/C₂ → C₃² ⊆ Aut C₂⁴	18	9+	C2^4:(C3xC6)	288,1029
C₂⁴⋊₂(C₃×C₆) = C₃×C₂⁴⋊C₆	φ: C₃×C₆/C₃ → C₆ ⊆ Aut C₂⁴	24	6	C2^4:2(C3xC6)	288,634
C₂⁴⋊₃(C₃×C₆) = C₃×D₄×A₄	φ: C₃×C₆/C₃ → C₆ ⊆ Aut C₂⁴	36	6	C2^4:3(C3xC6)	288,980
C₂⁴⋊₄(C₃×C₆) = A₄×C₂²×C₆	φ: C₃×C₆/C₆ → C₃ ⊆ Aut C₂⁴	72		C2^4:4(C3xC6)	288,1041
C₂⁴⋊₅(C₃×C₆) = C₆×C₂²⋊A₄	φ: C₃×C₆/C₆ → C₃ ⊆ Aut C₂⁴	36		C2^4:5(C3xC6)	288,1042
C₂⁴⋊₆(C₃×C₆) = C₃²×C₂²≀C₂	φ: C₃×C₆/C₃² → C₂ ⊆ Aut C₂⁴	72		C2^4:6(C3xC6)	288,817
C₂⁴⋊₇(C₃×C₆) = D₄×C₆²	φ: C₃×C₆/C₃² → C₂ ⊆ Aut C₂⁴	144		C2^4:7(C3xC6)	288,1019

Non-split extensions G=N.Q with N=C₂⁴ and Q=C₃×C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂⁴.(C₃×C₆) = A₄×C₂×C₁₂	φ: C₃×C₆/C₆ → C₃ ⊆ Aut C₂⁴	72		C2^4.(C3xC6)	288,979
C₂⁴.₂(C₃×C₆) = C₂²⋊C₄×C₃×C₆	φ: C₃×C₆/C₃² → C₂ ⊆ Aut C₂⁴	144		C2^4.2(C3xC6)	288,812

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