Extensions 1→N→G→Q→1 with N=C₃²⋊₄Q₈ and Q=C₆

Direct product G=N×Q with N=C₃²⋊₄Q₈ and Q=C₆

		d	ρ	Label	ID
C₆×C₃²⋊₄Q₈		144		C6xC3^2:4Q8	432,710

Semidirect products G=N:Q with N=C₃²⋊₄Q₈ and Q=C₆

extension	φ:Q→Out N	d	ρ	Label	ID
C₃²⋊₄Q₈⋊₁C₆ = He₃⋊₆SD₁₆	φ: C₆/C₁ → C₆ ⊆ Out C₃²⋊₄Q₈	72	6	C3^2:4Q8:1C6	432,117
C₃²⋊₄Q₈⋊₂C₆ = He₃⋊₈SD₁₆	φ: C₆/C₁ → C₆ ⊆ Out C₃²⋊₄Q₈	72	12-	C3^2:4Q8:2C6	432,152
C₃²⋊₄Q₈⋊₃C₆ = C₆².₁₃D₆	φ: C₆/C₁ → C₆ ⊆ Out C₃²⋊₄Q₈	72	12-	C3^2:4Q8:3C6	432,361
C₃²⋊₄Q₈⋊₄C₆ = Q₈×C₃²⋊C₆	φ: C₆/C₁ → C₆ ⊆ Out C₃²⋊₄Q₈	72	12-	C3^2:4Q8:4C6	432,368
C₃²⋊₄Q₈⋊₅C₆ = C₂×He₃⋊₃Q₈	φ: C₆/C₂ → C₃ ⊆ Out C₃²⋊₄Q₈	144		C3^2:4Q8:5C6	432,348
C₃²⋊₄Q₈⋊₆C₆ = C₆².₃₆D₆	φ: C₆/C₂ → C₃ ⊆ Out C₃²⋊₄Q₈	72	6	C3^2:4Q8:6C6	432,351
C₃²⋊₄Q₈⋊₇C₆ = C₃×C₂₄⋊₂S₃	φ: C₆/C₃ → C₂ ⊆ Out C₃²⋊₄Q₈	144		C3^2:4Q8:7C6	432,482
C₃²⋊₄Q₈⋊₈C₆ = C₃×D₁₂.S₃	φ: C₆/C₃ → C₂ ⊆ Out C₃²⋊₄Q₈	48	4	C3^2:4Q8:8C6	432,421
C₃²⋊₄Q₈⋊₉C₆ = C₃×C₃²⋊₉SD₁₆	φ: C₆/C₃ → C₂ ⊆ Out C₃²⋊₄Q₈	72		C3^2:4Q8:9C6	432,492
C₃²⋊₄Q₈⋊₁₀C₆ = C₃×S₃×Dic₆	φ: C₆/C₃ → C₂ ⊆ Out C₃²⋊₄Q₈	48	4	C3^2:4Q8:10C6	432,642
C₃²⋊₄Q₈⋊₁₁C₆ = C₃×D₁₂⋊₅S₃	φ: C₆/C₃ → C₂ ⊆ Out C₃²⋊₄Q₈	48	4	C3^2:4Q8:11C6	432,643
C₃²⋊₄Q₈⋊₁₂C₆ = C₃×C₁₂.D₆	φ: C₆/C₃ → C₂ ⊆ Out C₃²⋊₄Q₈	72		C3^2:4Q8:12C6	432,715
C₃²⋊₄Q₈⋊₁₃C₆ = C₃×Q₈×C₃⋊S₃	φ: C₆/C₃ → C₂ ⊆ Out C₃²⋊₄Q₈	144		C3^2:4Q8:13C6	432,716
C₃²⋊₄Q₈⋊₁₄C₆ = C₃×C₁₂.₅₉D₆	φ: trivial image	72		C3^2:4Q8:14C6	432,713

Non-split extensions G=N.Q with N=C₃²⋊₄Q₈ and Q=C₆

extension	φ:Q→Out N	d	ρ	Label	ID
C₃²⋊₄Q₈.₁C₆ = He₃⋊₄Q₁₆	φ: C₆/C₁ → C₆ ⊆ Out C₃²⋊₄Q₈	144	6-	C3^2:4Q8.1C6	432,114
C₃²⋊₄Q₈.₂C₆ = He₃⋊₆Q₁₆	φ: C₆/C₁ → C₆ ⊆ Out C₃²⋊₄Q₈	144	12-	C3^2:4Q8.2C6	432,160
C₃²⋊₄Q₈.₃C₆ = C₃×C₃²⋊₅Q₁₆	φ: C₆/C₃ → C₂ ⊆ Out C₃²⋊₄Q₈	144		C3^2:4Q8.3C6	432,484
C₃²⋊₄Q₈.₄C₆ = C₃×C₃²⋊₃Q₁₆	φ: C₆/C₃ → C₂ ⊆ Out C₃²⋊₄Q₈	48	4	C3^2:4Q8.4C6	432,424
C₃²⋊₄Q₈.₅C₆ = C₃×C₃²⋊₇Q₁₆	φ: C₆/C₃ → C₂ ⊆ Out C₃²⋊₄Q₈	144		C3^2:4Q8.5C6	432,494

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