Extensions 1→N→G→Q→1 with N=C₃²⋊C₆⋊C₄ and Q=C₂

Direct product G=N×Q with N=C₃²⋊C₆⋊C₄ and Q=C₂

		d	ρ	Label	ID
C₂×C₃²⋊C₆⋊C₄		72		C2xC3^2:C6:C4	432,317

Semidirect products G=N:Q with N=C₃²⋊C₆⋊C₄ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
C₃²⋊C₆⋊C₄⋊₁C₂ = C₁₂⋊S₃⋊S₃	φ: C₂/C₁ → C₂ ⊆ Out C₃²⋊C₆⋊C₄	72	12+	C3^2:C6:C4:1C2	432,295
C₃²⋊C₆⋊C₄⋊₂C₂ = C₁₂.₈₄(S₃²)	φ: C₂/C₁ → C₂ ⊆ Out C₃²⋊C₆⋊C₄	72	6	C3^2:C6:C4:2C2	432,296
C₃²⋊C₆⋊C₄⋊₃C₂ = C₆².₈D₆	φ: C₂/C₁ → C₂ ⊆ Out C₃²⋊C₆⋊C₄	72	12-	C3^2:C6:C4:3C2	432,318
C₃²⋊C₆⋊C₄⋊₄C₂ = C₆².₉D₆	φ: C₂/C₁ → C₂ ⊆ Out C₃²⋊C₆⋊C₄	72	6	C3^2:C6:C4:4C2	432,319
C₃²⋊C₆⋊C₄⋊₅C₂ = C₆²⋊D₆	φ: C₂/C₁ → C₂ ⊆ Out C₃²⋊C₆⋊C₄	36	12+	C3^2:C6:C4:5C2	432,323
C₃²⋊C₆⋊C₄⋊₆C₂ = C₄×C₃²⋊D₆	φ: trivial image	36	6	C3^2:C6:C4:6C2	432,300

Non-split extensions G=N.Q with N=C₃²⋊C₆⋊C₄ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
C₃²⋊C₆⋊C₄.C₂ = C₃⋊S₃⋊Dic₆	φ: C₂/C₁ → C₂ ⊆ Out C₃²⋊C₆⋊C₄	72	12-	C3^2:C6:C4.C2	432,294

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