Extensions 1→N→G→Q→1 with N=C₁₂ and Q=S₃²

Direct product G=N×Q with N=C₁₂ and Q=S₃²

		d	ρ	Label	ID
S₃²×C₁₂		48	4	S3^2xC12	432,648

Semidirect products G=N:Q with N=C₁₂ and Q=S₃²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₂⋊₁S₃² = C₃⋊S₃×D₁₂	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	72		C12:1S3^2	432,672
C₁₂⋊₂S₃² = C₁₂⋊S₃²	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	72		C12:2S3^2	432,673
C₁₂⋊₃S₃² = C₁₂⋊₃S₃²	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	48	4	C12:3S3^2	432,691
C₁₂⋊₄S₃² = S₃×C₁₂⋊S₃	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	72		C12:4S3^2	432,671
C₁₂⋊₅S₃² = C₄×S₃×C₃⋊S₃	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	72		C12:5S3^2	432,670
C₁₂⋊₆S₃² = C₃×S₃×D₁₂	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	48	4	C12:6S3^2	432,649
C₁₂⋊₇S₃² = C₄×C₃²⋊₄D₆	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₁₂	48	4	C12:7S3^2	432,690
C₁₂⋊₈S₃² = C₃×D₆⋊D₆	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₁₂	48	4	C12:8S3^2	432,650

Non-split extensions G=N.Q with N=C₁₂ and Q=S₃²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₂.₁S₃² = D₃₆⋊S₃	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	144	4	C12.1S3^2	432,68
C₁₂.₂S₃² = C₉⋊D₂₄	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	72	4+	C12.2S3^2	432,69
C₁₂.₃S₃² = D₁₂.D₉	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	144	4	C12.3S3^2	432,70
C₁₂.₄S₃² = C₃₆.D₆	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	144	4-	C12.4S3^2	432,71
C₁₂.₅S₃² = Dic₆⋊D₉	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	144	4	C12.5S3^2	432,72
C₁₂.₆S₃² = C₁₈.D₁₂	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	72	4+	C12.6S3^2	432,73
C₁₂.₇S₃² = C₁₂.D₁₈	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	144	4	C12.7S3^2	432,74
C₁₂.₈S₃² = C₉⋊Dic₁₂	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	144	4-	C12.8S3^2	432,75
C₁₂.₉S₃² = He₃⋊₃D₈	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	72	12+	C12.9S3^2	432,83
C₁₂.₁₀S₃² = He₃⋊₄SD₁₆	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	72	12-	C12.10S3^2	432,84
C₁₂.₁₁S₃² = He₃⋊₅SD₁₆	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	72	12+	C12.11S3^2	432,85
C₁₂.₁₂S₃² = He₃⋊₃Q₁₆	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	144	12-	C12.12S3^2	432,86
C₁₂.₁₃S₃² = D₉×Dic₆	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	144	4-	C12.13S3^2	432,280
C₁₂.₁₄S₃² = D₁₈.D₆	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	72	4	C12.14S3^2	432,281
C₁₂.₁₅S₃² = Dic₆⋊₅D₉	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	72	4+	C12.15S3^2	432,282
C₁₂.₁₆S₃² = Dic₁₈⋊S₃	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	72	4	C12.16S3^2	432,283
C₁₂.₁₇S₃² = D₁₂⋊₅D₉	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	144	4-	C12.17S3^2	432,285
C₁₂.₁₈S₃² = D₁₂⋊D₉	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	72	4	C12.18S3^2	432,286
C₁₂.₁₉S₃² = D₉×D₁₂	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	72	4+	C12.19S3^2	432,292
C₁₂.₂₀S₃² = C₃₆⋊D₆	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	72	4	C12.20S3^2	432,293
C₁₂.₂₁S₃² = C₃⋊S₃⋊Dic₆	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	72	12-	C12.21S3^2	432,294
C₁₂.₂₂S₃² = C₁₂⋊S₃⋊S₃	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	72	12+	C12.22S3^2	432,295
C₁₂.₂₃S₃² = C₁₂.S₃²	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	72	12-	C12.23S3^2	432,299
C₁₂.₂₄S₃² = C₃⋊S₃⋊D₁₂	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	36	12+	C12.24S3^2	432,301
C₁₂.₂₅S₃² = C₃³⋊₆D₈	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	144		C12.25S3^2	432,436
C₁₂.₂₆S₃² = C₃³⋊₇D₈	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	72		C12.26S3^2	432,437
C₁₂.₂₇S₃² = C₃³⋊₁₂SD₁₆	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	144		C12.27S3^2	432,439
C₁₂.₂₈S₃² = C₃³⋊₁₃SD₁₆	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	144		C12.28S3^2	432,440
C₁₂.₂₉S₃² = C₃³⋊₁₄SD₁₆	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	144		C12.29S3^2	432,441
C₁₂.₃₀S₃² = C₃³⋊₁₅SD₁₆	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	72		C12.30S3^2	432,442
C₁₂.₃₁S₃² = C₃³⋊₆Q₁₆	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	144		C12.31S3^2	432,445
C₁₂.₃₂S₃² = C₃³⋊₇Q₁₆	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	144		C12.32S3^2	432,446
C₁₂.₃₃S₃² = C₃³⋊₉D₈	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	48	4	C12.33S3^2	432,457
C₁₂.₃₄S₃² = C₃³⋊₁₈SD₁₆	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	48	4	C12.34S3^2	432,458
C₁₂.₃₅S₃² = C₃³⋊₉Q₁₆	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	48	4	C12.35S3^2	432,459
C₁₂.₃₆S₃² = (C₃×D₁₂)⋊S₃	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	144		C12.36S3^2	432,661
C₁₂.₃₇S₃² = D₁₂⋊(C₃⋊S₃)	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	72		C12.37S3^2	432,662
C₁₂.₃₈S₃² = C₃⋊S₃×Dic₆	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	144		C12.38S3^2	432,663
C₁₂.₃₉S₃² = C₁₂.₃₉S₃²	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	72		C12.39S3^2	432,664
C₁₂.₄₀S₃² = C₁₂.₄₀S₃²	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	72		C12.40S3^2	432,665
C₁₂.₄₁S₃² = C₃²⋊₉(S₃×Q₈)	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	72		C12.41S3^2	432,666
C₁₂.₄₂S₃² = C₃⋊S₃⋊₄Dic₆	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	48	4	C12.42S3^2	432,687
C₁₂.₄₃S₃² = C₁₂⋊S₃⋊₁₂S₃	φ: S₃²/C₃² → C₂² ⊆ Aut C₁₂	48	4	C12.43S3^2	432,688
C₁₂.₄₄S₃² = D₃₆.S₃	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	144	4-	C12.44S3^2	432,62
C₁₂.₄₅S₃² = C₆.D₃₆	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	72	4+	C12.45S3^2	432,63
C₁₂.₄₆S₃² = C₃⋊D₇₂	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	72	4+	C12.46S3^2	432,64
C₁₂.₄₇S₃² = C₃⋊Dic₃₆	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	144	4-	C12.47S3^2	432,65
C₁₂.₄₈S₃² = S₃×Dic₁₈	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	144	4-	C12.48S3^2	432,284
C₁₂.₄₉S₃² = D₃₆⋊₅S₃	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	144	4-	C12.49S3^2	432,288
C₁₂.₅₀S₃² = Dic₉.D₆	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	72	4+	C12.50S3^2	432,289
C₁₂.₅₁S₃² = S₃×D₃₆	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	72	4+	C12.51S3^2	432,291
C₁₂.₅₂S₃² = C₃³⋊₈D₈	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	72		C12.52S3^2	432,438
C₁₂.₅₃S₃² = C₃³⋊₁₆SD₁₆	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	144		C12.53S3^2	432,443
C₁₂.₅₄S₃² = C₃³⋊₁₇SD₁₆	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	72		C12.54S3^2	432,444
C₁₂.₅₅S₃² = C₃³⋊₈Q₁₆	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	144		C12.55S3^2	432,447
C₁₂.₅₆S₃² = S₃×C₃²⋊₄Q₈	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	144		C12.56S3^2	432,660
C₁₂.₅₇S₃² = C₁₂.₅₇S₃²	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	144		C12.57S3^2	432,668
C₁₂.₅₈S₃² = C₁₂.₅₈S₃²	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	72		C12.58S3^2	432,669
C₁₂.₅₉S₃² = D₉×C₃⋊C₈	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	144	4	C12.59S3^2	432,58
C₁₂.₆₀S₃² = C₃₆.₃₈D₆	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	72	4	C12.60S3^2	432,59
C₁₂.₆₁S₃² = C₃₆.₃₉D₆	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	144	4	C12.61S3^2	432,60
C₁₂.₆₂S₃² = C₃₆.₄₀D₆	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	72	4	C12.62S3^2	432,61
C₁₂.₆₃S₃² = S₃×C₉⋊C₈	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	144	4	C12.63S3^2	432,66
C₁₂.₆₄S₃² = D₆.Dic₉	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	144	4	C12.64S3^2	432,67
C₁₂.₆₅S₃² = D₆.D₁₈	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	72	4	C12.65S3^2	432,287
C₁₂.₆₆S₃² = C₄×S₃×D₉	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	72	4	C12.66S3^2	432,290
C₁₂.₆₇S₃² = S₃×C₃²⋊₄C₈	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	144		C12.67S3^2	432,430
C₁₂.₆₈S₃² = C₃⋊S₃×C₃⋊C₈	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	144		C12.68S3^2	432,431
C₁₂.₆₉S₃² = C₁₂.₆₉S₃²	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	72		C12.69S3^2	432,432
C₁₂.₇₀S₃² = C₃³⋊₇M₄(2)	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	144		C12.70S3^2	432,433
C₁₂.₇₁S₃² = C₃³⋊₈M₄(2)	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	144		C12.71S3^2	432,434
C₁₂.₇₂S₃² = C₃³⋊₉M₄(2)	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	72		C12.72S3^2	432,435
C₁₂.₇₃S₃² = C₁₂.₇₃S₃²	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	72		C12.73S3^2	432,667
C₁₂.₇₄S₃² = C₃×C₃⋊D₂₄	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	48	4	C12.74S3^2	432,419
C₁₂.₇₅S₃² = C₃×D₁₂.S₃	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	48	4	C12.75S3^2	432,421
C₁₂.₇₆S₃² = C₃×C₃²⋊₅SD₁₆	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	48	4	C12.76S3^2	432,422
C₁₂.₇₇S₃² = C₃×C₃²⋊₃Q₁₆	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	48	4	C12.77S3^2	432,424
C₁₂.₇₈S₃² = C₃×S₃×Dic₆	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	48	4	C12.78S3^2	432,642
C₁₂.₇₉S₃² = C₃×D₁₂⋊₅S₃	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	48	4	C12.79S3^2	432,643
C₁₂.₈₀S₃² = C₃×D₆.₆D₆	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₂	48	4	C12.80S3^2	432,647
C₁₂.₈₁S₃² = He₃⋊₃SD₁₆	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₁₂	72	6	C12.81S3^2	432,78
C₁₂.₈₂S₃² = He₃⋊₂D₈	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₁₂	72	6+	C12.82S3^2	432,79
C₁₂.₈₃S₃² = He₃⋊₂Q₁₆	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₁₂	144	6-	C12.83S3^2	432,80
C₁₂.₈₄S₃² = C₁₂.₈₄S₃²	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₁₂	72	6	C12.84S3^2	432,296
C₁₂.₈₅S₃² = C₁₂.₈₅S₃²	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₁₂	72	6-	C12.85S3^2	432,298
C₁₂.₈₆S₃² = C₁₂.₈₆S₃²	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₁₂	36	6+	C12.86S3^2	432,302
C₁₂.₈₇S₃² = C₃²⋊C₆⋊C₈	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₁₂	72	6	C12.87S3^2	432,76
C₁₂.₈₈S₃² = He₃⋊M₄(2)	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₁₂	72	6	C12.88S3^2	432,77
C₁₂.₈₉S₃² = C₁₂.₈₉S₃²	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₁₂	72	6	C12.89S3^2	432,81
C₁₂.₉₀S₃² = He₃⋊₃M₄(2)	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₁₂	72	6	C12.90S3^2	432,82
C₁₂.₉₁S₃² = C₁₂.₉₁S₃²	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₁₂	72	6	C12.91S3^2	432,297
C₁₂.₉₂S₃² = C₄×C₃²⋊D₆	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₁₂	36	6	C12.92S3^2	432,300
C₁₂.₉₃S₃² = C₁₂.₉₃S₃²	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₁₂	48	4	C12.93S3^2	432,455
C₁₂.₉₄S₃² = C₃³⋊₁₀M₄(2)	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₁₂	48	4	C12.94S3^2	432,456
C₁₂.₉₅S₃² = C₁₂.₉₅S₃²	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₁₂	48	4	C12.95S3^2	432,689
C₁₂.₉₆S₃² = C₃×C₃²⋊₂D₈	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₁₂	48	4	C12.96S3^2	432,418
C₁₂.₉₇S₃² = C₃×Dic₆⋊S₃	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₁₂	48	4	C12.97S3^2	432,420
C₁₂.₉₈S₃² = C₃×C₃²⋊₂Q₁₆	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₁₂	48	4	C12.98S3^2	432,423
C₁₂.₉₉S₃² = C₃×D₁₂⋊S₃	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₁₂	48	4	C12.99S3^2	432,644
C₁₂.₁₀₀S₃² = C₃×Dic₃.D₆	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₁₂	48	4	C12.100S3^2	432,645
C₁₂.₁₀₁S₃² = C₃×S₃×C₃⋊C₈	central extension (φ=1)	48	4	C12.101S3^2	432,414
C₁₂.₁₀₂S₃² = C₃×C₁₂.₂₉D₆	central extension (φ=1)	48	4	C12.102S3^2	432,415
C₁₂.₁₀₃S₃² = C₃×D₆.Dic₃	central extension (φ=1)	48	4	C12.103S3^2	432,416
C₁₂.₁₀₄S₃² = C₃×C₁₂.₃₁D₆	central extension (φ=1)	48	4	C12.104S3^2	432,417
C₁₂.₁₀₅S₃² = C₃×D₆.D₆	central extension (φ=1)	48	4	C12.105S3^2	432,646

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Extensions 1→N→G→Q→1 with N=C12 and Q=S32

Extensions 1→N→G→Q→1 with N=C₁₂ and Q=S₃²