Extensions 1→N→G→Q→1 with N=C₄ and Q=C₃²⋊D₆

Direct product G=N×Q with N=C₄ and Q=C₃²⋊D₆

		d	ρ	Label	ID
C₄×C₃²⋊D₆		36	6	C4xC3^2:D6	432,300

Semidirect products G=N:Q with N=C₄ and Q=C₃²⋊D₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊₁(C₃²⋊D₆) = C₃⋊S₃⋊D₁₂	φ: C₃²⋊D₆/C₃²⋊C₆ → C₂ ⊆ Aut C₄	36	12+	C4:1(C3^2:D6)	432,301
C₄⋊₂(C₃²⋊D₆) = C₁₂.₈₆S₃²	φ: C₃²⋊D₆/He₃⋊C₂ → C₂ ⊆ Aut C₄	36	6+	C4:2(C3^2:D6)	432,302

Non-split extensions G=N.Q with N=C₄ and Q=C₃²⋊D₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁(C₃²⋊D₆) = He₃⋊₃D₈	φ: C₃²⋊D₆/C₃²⋊C₆ → C₂ ⊆ Aut C₄	72	12+	C4.1(C3^2:D6)	432,83
C₄.₂(C₃²⋊D₆) = He₃⋊₄SD₁₆	φ: C₃²⋊D₆/C₃²⋊C₆ → C₂ ⊆ Aut C₄	72	12-	C4.2(C3^2:D6)	432,84
C₄.₃(C₃²⋊D₆) = He₃⋊₅SD₁₆	φ: C₃²⋊D₆/C₃²⋊C₆ → C₂ ⊆ Aut C₄	72	12+	C4.3(C3^2:D6)	432,85
C₄.₄(C₃²⋊D₆) = He₃⋊₃Q₁₆	φ: C₃²⋊D₆/C₃²⋊C₆ → C₂ ⊆ Aut C₄	144	12-	C4.4(C3^2:D6)	432,86
C₄.₅(C₃²⋊D₆) = C₃⋊S₃⋊Dic₆	φ: C₃²⋊D₆/C₃²⋊C₆ → C₂ ⊆ Aut C₄	72	12-	C4.5(C3^2:D6)	432,294
C₄.₆(C₃²⋊D₆) = C₁₂⋊S₃⋊S₃	φ: C₃²⋊D₆/C₃²⋊C₆ → C₂ ⊆ Aut C₄	72	12+	C4.6(C3^2:D6)	432,295
C₄.₇(C₃²⋊D₆) = C₁₂.S₃²	φ: C₃²⋊D₆/C₃²⋊C₆ → C₂ ⊆ Aut C₄	72	12-	C4.7(C3^2:D6)	432,299
C₄.₈(C₃²⋊D₆) = He₃⋊₃SD₁₆	φ: C₃²⋊D₆/He₃⋊C₂ → C₂ ⊆ Aut C₄	72	6	C4.8(C3^2:D6)	432,78
C₄.₉(C₃²⋊D₆) = He₃⋊₂D₈	φ: C₃²⋊D₆/He₃⋊C₂ → C₂ ⊆ Aut C₄	72	6+	C4.9(C3^2:D6)	432,79
C₄.₁₀(C₃²⋊D₆) = He₃⋊₂Q₁₆	φ: C₃²⋊D₆/He₃⋊C₂ → C₂ ⊆ Aut C₄	144	6-	C4.10(C3^2:D6)	432,80
C₄.₁₁(C₃²⋊D₆) = C₁₂.₈₄S₃²	φ: C₃²⋊D₆/He₃⋊C₂ → C₂ ⊆ Aut C₄	72	6	C4.11(C3^2:D6)	432,296
C₄.₁₂(C₃²⋊D₆) = C₁₂.₈₅S₃²	φ: C₃²⋊D₆/He₃⋊C₂ → C₂ ⊆ Aut C₄	72	6-	C4.12(C3^2:D6)	432,298
C₄.₁₃(C₃²⋊D₆) = C₃²⋊C₆⋊C₈	central extension (φ=1)	72	6	C4.13(C3^2:D6)	432,76
C₄.₁₄(C₃²⋊D₆) = He₃⋊M₄(2)	central extension (φ=1)	72	6	C4.14(C3^2:D6)	432,77
C₄.₁₅(C₃²⋊D₆) = C₁₂.₈₉S₃²	central extension (φ=1)	72	6	C4.15(C3^2:D6)	432,81
C₄.₁₆(C₃²⋊D₆) = He₃⋊₃M₄(2)	central extension (φ=1)	72	6	C4.16(C3^2:D6)	432,82
C₄.₁₇(C₃²⋊D₆) = C₁₂.₉₁S₃²	central extension (φ=1)	72	6	C4.17(C3^2:D6)	432,297

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁