Extensions 1→N→G→Q→1 with N=C₃² and Q=Q₈⋊₂S₃

Direct product G=N×Q with N=C₃² and Q=Q₈⋊₂S₃

		d	ρ	Label	ID
C₃²×Q₈⋊₂S₃		144		C3^2xQ8:2S3	432,477

Semidirect products G=N:Q with N=C₃² and Q=Q₈⋊₂S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃²⋊(Q₈⋊₂S₃) = C₃³⋊₃SD₁₆	φ: Q₈⋊₂S₃/C₃ → SD₁₆ ⊆ Aut C₃²	24	16+	C3^2:(Q8:2S3)	432,739
C₃²⋊₂(Q₈⋊₂S₃) = He₃⋊₃SD₁₆	φ: Q₈⋊₂S₃/C₄ → D₆ ⊆ Aut C₃²	72	6	C3^2:2(Q8:2S3)	432,78
C₃²⋊₃(Q₈⋊₂S₃) = He₃⋊₄SD₁₆	φ: Q₈⋊₂S₃/C₄ → D₆ ⊆ Aut C₃²	72	12-	C3^2:3(Q8:2S3)	432,84
C₃²⋊₄(Q₈⋊₂S₃) = C₃³⋊₆SD₁₆	φ: Q₈⋊₂S₃/C₆ → D₄ ⊆ Aut C₃²	24	4	C3^2:4(Q8:2S3)	432,583
C₃²⋊₅(Q₈⋊₂S₃) = He₃⋊₁₀SD₁₆	φ: Q₈⋊₂S₃/Q₈ → S₃ ⊆ Aut C₃²	72	12+	C3^2:5(Q8:2S3)	432,161
C₃²⋊₆(Q₈⋊₂S₃) = He₃⋊₁₁SD₁₆	φ: Q₈⋊₂S₃/Q₈ → S₃ ⊆ Aut C₃²	72	6	C3^2:6(Q8:2S3)	432,196
C₃²⋊₇(Q₈⋊₂S₃) = C₃³⋊₁₃SD₁₆	φ: Q₈⋊₂S₃/C₁₂ → C₂² ⊆ Aut C₃²	144		C3^2:7(Q8:2S3)	432,440
C₃²⋊₈(Q₈⋊₂S₃) = C₃³⋊₁₅SD₁₆	φ: Q₈⋊₂S₃/C₁₂ → C₂² ⊆ Aut C₃²	72		C3^2:8(Q8:2S3)	432,442
C₃²⋊₉(Q₈⋊₂S₃) = C₃³⋊₁₈SD₁₆	φ: Q₈⋊₂S₃/C₁₂ → C₂² ⊆ Aut C₃²	48	4	C3^2:9(Q8:2S3)	432,458
C₃²⋊₁₀(Q₈⋊₂S₃) = C₃×C₃²⋊₅SD₁₆	φ: Q₈⋊₂S₃/C₃⋊C₈ → C₂ ⊆ Aut C₃²	48	4	C3^2:10(Q8:2S3)	432,422
C₃²⋊₁₁(Q₈⋊₂S₃) = C₃³⋊₁₇SD₁₆	φ: Q₈⋊₂S₃/C₃⋊C₈ → C₂ ⊆ Aut C₃²	72		C3^2:11(Q8:2S3)	432,444
C₃²⋊₁₂(Q₈⋊₂S₃) = C₃×Dic₆⋊S₃	φ: Q₈⋊₂S₃/D₁₂ → C₂ ⊆ Aut C₃²	48	4	C3^2:12(Q8:2S3)	432,420
C₃²⋊₁₃(Q₈⋊₂S₃) = C₃³⋊₁₂SD₁₆	φ: Q₈⋊₂S₃/D₁₂ → C₂ ⊆ Aut C₃²	144		C3^2:13(Q8:2S3)	432,439
C₃²⋊₁₄(Q₈⋊₂S₃) = C₃×C₃²⋊₁₁SD₁₆	φ: Q₈⋊₂S₃/C₃×Q₈ → C₂ ⊆ Aut C₃²	144		C3^2:14(Q8:2S3)	432,493
C₃²⋊₁₅(Q₈⋊₂S₃) = C₃³⋊₂₇SD₁₆	φ: Q₈⋊₂S₃/C₃×Q₈ → C₂ ⊆ Aut C₃²	216		C3^2:15(Q8:2S3)	432,509

Non-split extensions G=N.Q with N=C₃² and Q=Q₈⋊₂S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃².(Q₈⋊₂S₃) = D₃₆.C₆	φ: Q₈⋊₂S₃/Q₈ → S₃ ⊆ Aut C₃²	72	12+	C3^2.(Q8:2S3)	432,163
C₃².₂(Q₈⋊₂S₃) = Dic₆⋊D₉	φ: Q₈⋊₂S₃/C₁₂ → C₂² ⊆ Aut C₃²	144	4	C3^2.2(Q8:2S3)	432,72
C₃².₃(Q₈⋊₂S₃) = C₁₈.D₁₂	φ: Q₈⋊₂S₃/C₁₂ → C₂² ⊆ Aut C₃²	72	4+	C3^2.3(Q8:2S3)	432,73
C₃².₄(Q₈⋊₂S₃) = C₃×Q₈⋊₂D₉	φ: Q₈⋊₂S₃/C₃×Q₈ → C₂ ⊆ Aut C₃²	144	4	C3^2.4(Q8:2S3)	432,157
C₃².₅(Q₈⋊₂S₃) = C₃₆.₂₀D₆	φ: Q₈⋊₂S₃/C₃×Q₈ → C₂ ⊆ Aut C₃²	216		C3^2.5(Q8:2S3)	432,195

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁