Extensions 1→N→G→Q→1 with N=C₂³ and Q=C₃²⋊C₆

Direct product G=N×Q with N=C₂³ and Q=C₃²⋊C₆

		d	ρ	Label	ID
C₂³×C₃²⋊C₆		72		C2^3xC3^2:C6	432,558

Semidirect products G=N:Q with N=C₂³ and Q=C₃²⋊C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³⋊(C₃²⋊C₆) = C₂×C₆²⋊S₃	φ: C₃²⋊C₆/C₃² → S₃ ⊆ Aut C₂³	18	6+	C2^3:(C3^2:C6)	432,535
C₂³⋊₂(C₃²⋊C₆) = C₂×C₆²⋊C₆	φ: C₃²⋊C₆/C₃⋊S₃ → C₃ ⊆ Aut C₂³	18	6+	C2^3:2(C3^2:C6)	432,542
C₂³⋊₃(C₃²⋊C₆) = C₂×He₃⋊₆D₄	φ: C₃²⋊C₆/He₃ → C₂ ⊆ Aut C₂³	72		C2^3:3(C3^2:C6)	432,377

Non-split extensions G=N.Q with N=C₂³ and Q=C₃²⋊C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³.(C₃²⋊C₆) = C₆²⋊₅Dic₃	φ: C₃²⋊C₆/C₃² → S₃ ⊆ Aut C₂³	36	6-	C2^3.(C3^2:C6)	432,251
C₂³.₂(C₃²⋊C₆) = C₆²⋊₄C₁₂	φ: C₃²⋊C₆/C₃⋊S₃ → C₃ ⊆ Aut C₂³	36	6-	C2^3.2(C3^2:C6)	432,272
C₂³.₃(C₃²⋊C₆) = C₆²⋊₃C₁₂	φ: C₃²⋊C₆/He₃ → C₂ ⊆ Aut C₂³	72		C2^3.3(C3^2:C6)	432,166
C₂³.₄(C₃²⋊C₆) = C₂²×C₃²⋊C₁₂	central extension (φ=1)	144		C2^3.4(C3^2:C6)	432,376

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