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

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

		d	ρ	Label	ID
C₄×C₃²⋊C₆		36	6	C4xC3^2:C6	216,50

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊(C₃²⋊C₆) = He₃⋊₄D₄	φ: C₃²⋊C₆/He₃ → C₂ ⊆ Aut C₄	36	6+	C4:(C3^2:C6)	216,51

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.(C₃²⋊C₆) = He₃⋊₃Q₈	φ: C₃²⋊C₆/He₃ → C₂ ⊆ Aut C₄	72	6-	C4.(C3^2:C6)	216,49
C₄.₂(C₃²⋊C₆) = He₃⋊₃C₈	central extension (φ=1)	72	6	C4.2(C3^2:C6)	216,14

⋊

ℤ

𝔽

○

≀

ℚ

◁

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