Extensions 1→N→G→Q→1 with N=C₆ and Q=C₃×M₄(2)

Direct product G=N×Q with N=C₆ and Q=C₃×M₄(2)

		d	ρ	Label	ID
M₄(2)×C₃×C₆		144		M4(2)xC3xC6	288,827

Semidirect products G=N:Q with N=C₆ and Q=C₃×M₄(2)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆⋊₁(C₃×M₄(2)) = C₆×C₈⋊S₃	φ: C₃×M₄(2)/C₂₄ → C₂ ⊆ Aut C₆	96		C6:1(C3xM4(2))	288,671
C₆⋊₂(C₃×M₄(2)) = C₆×C₄.Dic₃	φ: C₃×M₄(2)/C₂×C₁₂ → C₂ ⊆ Aut C₆	48		C6:2(C3xM4(2))	288,692

Non-split extensions G=N.Q with N=C₆ and Q=C₃×M₄(2)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆.₁(C₃×M₄(2)) = C₃×Dic₃⋊C₈	φ: C₃×M₄(2)/C₂₄ → C₂ ⊆ Aut C₆	96		C6.1(C3xM4(2))	288,248
C₆.₂(C₃×M₄(2)) = C₃×C₂₄⋊C₄	φ: C₃×M₄(2)/C₂₄ → C₂ ⊆ Aut C₆	96		C6.2(C3xM4(2))	288,249
C₆.₃(C₃×M₄(2)) = C₃×D₆⋊C₈	φ: C₃×M₄(2)/C₂₄ → C₂ ⊆ Aut C₆	96		C6.3(C3xM4(2))	288,254
C₆.₄(C₃×M₄(2)) = C₃×C₄².S₃	φ: C₃×M₄(2)/C₂×C₁₂ → C₂ ⊆ Aut C₆	96		C6.4(C3xM4(2))	288,237
C₆.₅(C₃×M₄(2)) = C₃×C₁₂⋊C₈	φ: C₃×M₄(2)/C₂×C₁₂ → C₂ ⊆ Aut C₆	96		C6.5(C3xM4(2))	288,238
C₆.₆(C₃×M₄(2)) = C₃×C₁₂.₅₅D₄	φ: C₃×M₄(2)/C₂×C₁₂ → C₂ ⊆ Aut C₆	48		C6.6(C3xM4(2))	288,264
C₆.₇(C₃×M₄(2)) = C₉×C₈⋊C₄	central extension (φ=1)	288		C6.7(C3xM4(2))	288,47
C₆.₈(C₃×M₄(2)) = C₉×C₂²⋊C₈	central extension (φ=1)	144		C6.8(C3xM4(2))	288,48
C₆.₉(C₃×M₄(2)) = C₉×C₄⋊C₈	central extension (φ=1)	288		C6.9(C3xM4(2))	288,55
C₆.₁₀(C₃×M₄(2)) = M₄(2)×C₁₈	central extension (φ=1)	144		C6.10(C3xM4(2))	288,180
C₆.₁₁(C₃×M₄(2)) = C₃²×C₈⋊C₄	central extension (φ=1)	288		C6.11(C3xM4(2))	288,315
C₆.₁₂(C₃×M₄(2)) = C₃²×C₂²⋊C₈	central extension (φ=1)	144		C6.12(C3xM4(2))	288,316
C₆.₁₃(C₃×M₄(2)) = C₃²×C₄⋊C₈	central extension (φ=1)	288		C6.13(C3xM4(2))	288,323

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