Extensions 1→N→G→Q→1 with N=C₃² and Q=C₃×M₄(2)

Direct product G=N×Q with N=C₃² and Q=C₃×M₄(2)

		d	ρ	Label	ID
M₄(2)×C₃³		216		M4(2)xC3^3	432,516

Semidirect products G=N:Q with N=C₃² and Q=C₃×M₄(2)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃²⋊₁(C₃×M₄(2)) = He₃⋊₅M₄(2)	φ: C₃×M₄(2)/C₈ → C₆ ⊆ Aut C₃²	72	6	C3^2:1(C3xM4(2))	432,116
C₃²⋊₂(C₃×M₄(2)) = He₃⋊₇M₄(2)	φ: C₃×M₄(2)/C₂×C₄ → C₆ ⊆ Aut C₃²	72	6	C3^2:2(C3xM4(2))	432,137
C₃²⋊₃(C₃×M₄(2)) = C₃×C₃²⋊M₄(2)	φ: C₃×M₄(2)/C₁₂ → C₄ ⊆ Aut C₃²	48	4	C3^2:3(C3xM4(2))	432,629
C₃²⋊₄(C₃×M₄(2)) = C₃×D₆.Dic₃	φ: C₃×M₄(2)/C₁₂ → C₂² ⊆ Aut C₃²	48	4	C3^2:4(C3xM4(2))	432,416
C₃²⋊₅(C₃×M₄(2)) = C₃×C₁₂.₃₁D₆	φ: C₃×M₄(2)/C₁₂ → C₂² ⊆ Aut C₃²	48	4	C3^2:5(C3xM4(2))	432,417
C₃²⋊₆(C₃×M₄(2)) = C₃×C₆².C₄	φ: C₃×M₄(2)/C₂×C₆ → C₄ ⊆ Aut C₃²	24	4	C3^2:6(C3xM4(2))	432,633
C₃²⋊₇(C₃×M₄(2)) = M₄(2)×He₃	φ: C₃×M₄(2)/M₄(2) → C₃ ⊆ Aut C₃²	72	6	C3^2:7(C3xM4(2))	432,213
C₃²⋊₈(C₃×M₄(2)) = C₃²×C₈⋊S₃	φ: C₃×M₄(2)/C₂₄ → C₂ ⊆ Aut C₃²	144		C3^2:8(C3xM4(2))	432,465
C₃²⋊₉(C₃×M₄(2)) = C₃×C₂₄⋊S₃	φ: C₃×M₄(2)/C₂₄ → C₂ ⊆ Aut C₃²	144		C3^2:9(C3xM4(2))	432,481
C₃²⋊₁₀(C₃×M₄(2)) = C₃²×C₄.Dic₃	φ: C₃×M₄(2)/C₂×C₁₂ → C₂ ⊆ Aut C₃²	72		C3^2:10(C3xM4(2))	432,470
C₃²⋊₁₁(C₃×M₄(2)) = C₃×C₁₂.₅₈D₆	φ: C₃×M₄(2)/C₂×C₁₂ → C₂ ⊆ Aut C₃²	72		C3^2:11(C3xM4(2))	432,486

Non-split extensions G=N.Q with N=C₃² and Q=C₃×M₄(2)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃².(C₃×M₄(2)) = M₄(2)×3_-¹⁺²	φ: C₃×M₄(2)/M₄(2) → C₃ ⊆ Aut C₃²	72	6	C3^2.(C3xM4(2))	432,214
C₃².₂(C₃×M₄(2)) = C₉×C₈⋊S₃	φ: C₃×M₄(2)/C₂₄ → C₂ ⊆ Aut C₃²	144	2	C3^2.2(C3xM4(2))	432,110
C₃².₃(C₃×M₄(2)) = C₉×C₄.Dic₃	φ: C₃×M₄(2)/C₂×C₁₂ → C₂ ⊆ Aut C₃²	72	2	C3^2.3(C3xM4(2))	432,127
C₃².₄(C₃×M₄(2)) = M₄(2)×C₃×C₉	central extension (φ=1)	216		C3^2.4(C3xM4(2))	432,212

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