Extensions 1→N→G→Q→1 with N=C₄₂ and Q=D₄

Direct product G=N×Q with N=C₄₂ and Q=D₄

		d	ρ	Label	ID
D₄×C₄₂		168		D4xC42	336,205

Semidirect products G=N:Q with N=C₄₂ and Q=D₄

extension	φ:Q→Aut N	d	Label	ID
C₄₂⋊₁D₄ = C₂×C₂₁⋊D₄	φ: D₄/C₂ → C₂² ⊆ Aut C₄₂	168	C42:1D4	336,157
C₄₂⋊₂D₄ = C₂×C₃⋊D₂₈	φ: D₄/C₂ → C₂² ⊆ Aut C₄₂	168	C42:2D4	336,158
C₄₂⋊₃D₄ = C₂×C₇⋊D₁₂	φ: D₄/C₂ → C₂² ⊆ Aut C₄₂	168	C42:3D4	336,159
C₄₂⋊₄D₄ = C₂×D₈₄	φ: D₄/C₄ → C₂ ⊆ Aut C₄₂	168	C42:4D4	336,196
C₄₂⋊₅D₄ = C₆×D₂₈	φ: D₄/C₄ → C₂ ⊆ Aut C₄₂	168	C42:5D4	336,176
C₄₂⋊₆D₄ = C₁₄×D₁₂	φ: D₄/C₄ → C₂ ⊆ Aut C₄₂	168	C42:6D4	336,186
C₄₂⋊₇D₄ = C₂×C₂₁⋊₇D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₄₂	168	C42:7D4	336,203
C₄₂⋊₈D₄ = C₆×C₇⋊D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₄₂	168	C42:8D4	336,183
C₄₂⋊₉D₄ = C₁₄×C₃⋊D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₄₂	168	C42:9D4	336,193

Non-split extensions G=N.Q with N=C₄₂ and Q=D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄₂.₁D₄ = C₂₁⋊D₈	φ: D₄/C₂ → C₂² ⊆ Aut C₄₂	168	4	C42.1D4	336,29
C₄₂.₂D₄ = C₃⋊D₅₆	φ: D₄/C₂ → C₂² ⊆ Aut C₄₂	168	4+	C42.2D4	336,30
C₄₂.₃D₄ = C₇⋊D₂₄	φ: D₄/C₂ → C₂² ⊆ Aut C₄₂	168	4+	C42.3D4	336,31
C₄₂.₄D₄ = C₂₈.D₆	φ: D₄/C₂ → C₂² ⊆ Aut C₄₂	168	4	C42.4D4	336,32
C₄₂.₅D₄ = C₄₂.D₄	φ: D₄/C₂ → C₂² ⊆ Aut C₄₂	168	4	C42.5D4	336,33
C₄₂.₆D₄ = C₆.D₂₈	φ: D₄/C₂ → C₂² ⊆ Aut C₄₂	168	4-	C42.6D4	336,34
C₄₂.₇D₄ = C₂₁⋊SD₁₆	φ: D₄/C₂ → C₂² ⊆ Aut C₄₂	168	4+	C42.7D4	336,35
C₄₂.₈D₄ = D₁₂.D₇	φ: D₄/C₂ → C₂² ⊆ Aut C₄₂	168	4-	C42.8D4	336,36
C₄₂.₉D₄ = Dic₆⋊D₇	φ: D₄/C₂ → C₂² ⊆ Aut C₄₂	168	4+	C42.9D4	336,37
C₄₂.₁₀D₄ = C₂₁⋊Q₁₆	φ: D₄/C₂ → C₂² ⊆ Aut C₄₂	336	4	C42.10D4	336,38
C₄₂.₁₁D₄ = C₃⋊Dic₂₈	φ: D₄/C₂ → C₂² ⊆ Aut C₄₂	336	4-	C42.11D4	336,39
C₄₂.₁₂D₄ = C₇⋊Dic₁₂	φ: D₄/C₂ → C₂² ⊆ Aut C₄₂	336	4-	C42.12D4	336,40
C₄₂.₁₃D₄ = D₁₄⋊Dic₃	φ: D₄/C₂ → C₂² ⊆ Aut C₄₂	168		C42.13D4	336,42
C₄₂.₁₄D₄ = D₆⋊Dic₇	φ: D₄/C₂ → C₂² ⊆ Aut C₄₂	168		C42.14D4	336,43
C₄₂.₁₅D₄ = D₄₂⋊C₄	φ: D₄/C₂ → C₂² ⊆ Aut C₄₂	168		C42.15D4	336,44
C₄₂.₁₆D₄ = C₄₂.Q₈	φ: D₄/C₂ → C₂² ⊆ Aut C₄₂	336		C42.16D4	336,45
C₄₂.₁₇D₄ = Dic₂₁⋊C₄	φ: D₄/C₂ → C₂² ⊆ Aut C₄₂	336		C42.17D4	336,46
C₄₂.₁₈D₄ = C₁₄.Dic₆	φ: D₄/C₂ → C₂² ⊆ Aut C₄₂	336		C42.18D4	336,47
C₄₂.₁₉D₄ = C₈⋊D₂₁	φ: D₄/C₄ → C₂ ⊆ Aut C₄₂	168	2	C42.19D4	336,92
C₄₂.₂₀D₄ = D₁₆₈	φ: D₄/C₄ → C₂ ⊆ Aut C₄₂	168	2+	C42.20D4	336,93
C₄₂.₂₁D₄ = Dic₈₄	φ: D₄/C₄ → C₂ ⊆ Aut C₄₂	336	2-	C42.21D4	336,94
C₄₂.₂₂D₄ = C₈₄⋊C₄	φ: D₄/C₄ → C₂ ⊆ Aut C₄₂	336		C42.22D4	336,99
C₄₂.₂₃D₄ = C₃×C₅₆⋊C₂	φ: D₄/C₄ → C₂ ⊆ Aut C₄₂	168	2	C42.23D4	336,60
C₄₂.₂₄D₄ = C₃×D₅₆	φ: D₄/C₄ → C₂ ⊆ Aut C₄₂	168	2	C42.24D4	336,61
C₄₂.₂₅D₄ = C₃×Dic₂₈	φ: D₄/C₄ → C₂ ⊆ Aut C₄₂	336	2	C42.25D4	336,62
C₄₂.₂₆D₄ = C₃×C₄⋊Dic₇	φ: D₄/C₄ → C₂ ⊆ Aut C₄₂	336		C42.26D4	336,67
C₄₂.₂₇D₄ = C₃×D₁₄⋊C₄	φ: D₄/C₄ → C₂ ⊆ Aut C₄₂	168		C42.27D4	336,68
C₄₂.₂₈D₄ = C₇×C₂₄⋊C₂	φ: D₄/C₄ → C₂ ⊆ Aut C₄₂	168	2	C42.28D4	336,76
C₄₂.₂₉D₄ = C₇×D₂₄	φ: D₄/C₄ → C₂ ⊆ Aut C₄₂	168	2	C42.29D4	336,77
C₄₂.₃₀D₄ = C₇×Dic₁₂	φ: D₄/C₄ → C₂ ⊆ Aut C₄₂	336	2	C42.30D4	336,78
C₄₂.₃₁D₄ = C₇×C₄⋊Dic₃	φ: D₄/C₄ → C₂ ⊆ Aut C₄₂	336		C42.31D4	336,83
C₄₂.₃₂D₄ = C₄₂.₄Q₈	φ: D₄/C₂² → C₂ ⊆ Aut C₄₂	336		C42.32D4	336,98
C₄₂.₃₃D₄ = C₂.D₈₄	φ: D₄/C₂² → C₂ ⊆ Aut C₄₂	168		C42.33D4	336,100
C₄₂.₃₄D₄ = D₄⋊D₂₁	φ: D₄/C₂² → C₂ ⊆ Aut C₄₂	168	4+	C42.34D4	336,101
C₄₂.₃₅D₄ = D₄.D₂₁	φ: D₄/C₂² → C₂ ⊆ Aut C₄₂	168	4-	C42.35D4	336,102
C₄₂.₃₆D₄ = Q₈⋊₂D₂₁	φ: D₄/C₂² → C₂ ⊆ Aut C₄₂	168	4+	C42.36D4	336,103
C₄₂.₃₇D₄ = C₂₁⋊₇Q₁₆	φ: D₄/C₂² → C₂ ⊆ Aut C₄₂	336	4-	C42.37D4	336,104
C₄₂.₃₈D₄ = C₄₂.₃₈D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₄₂	168		C42.38D4	336,105
C₄₂.₃₉D₄ = C₃×Dic₇⋊C₄	φ: D₄/C₂² → C₂ ⊆ Aut C₄₂	336		C42.39D4	336,66
C₄₂.₄₀D₄ = C₃×D₄⋊D₇	φ: D₄/C₂² → C₂ ⊆ Aut C₄₂	168	4	C42.40D4	336,69
C₄₂.₄₁D₄ = C₃×D₄.D₇	φ: D₄/C₂² → C₂ ⊆ Aut C₄₂	168	4	C42.41D4	336,70
C₄₂.₄₂D₄ = C₃×Q₈⋊D₇	φ: D₄/C₂² → C₂ ⊆ Aut C₄₂	168	4	C42.42D4	336,71
C₄₂.₄₃D₄ = C₃×C₇⋊Q₁₆	φ: D₄/C₂² → C₂ ⊆ Aut C₄₂	336	4	C42.43D4	336,72
C₄₂.₄₄D₄ = C₃×C₂³.D₇	φ: D₄/C₂² → C₂ ⊆ Aut C₄₂	168		C42.44D4	336,73
C₄₂.₄₅D₄ = C₇×Dic₃⋊C₄	φ: D₄/C₂² → C₂ ⊆ Aut C₄₂	336		C42.45D4	336,82
C₄₂.₄₆D₄ = C₇×D₆⋊C₄	φ: D₄/C₂² → C₂ ⊆ Aut C₄₂	168		C42.46D4	336,84
C₄₂.₄₇D₄ = C₇×D₄⋊S₃	φ: D₄/C₂² → C₂ ⊆ Aut C₄₂	168	4	C42.47D4	336,85
C₄₂.₄₈D₄ = C₇×D₄.S₃	φ: D₄/C₂² → C₂ ⊆ Aut C₄₂	168	4	C42.48D4	336,86
C₄₂.₄₉D₄ = C₇×Q₈⋊₂S₃	φ: D₄/C₂² → C₂ ⊆ Aut C₄₂	168	4	C42.49D4	336,87
C₄₂.₅₀D₄ = C₇×C₃⋊Q₁₆	φ: D₄/C₂² → C₂ ⊆ Aut C₄₂	336	4	C42.50D4	336,88
C₄₂.₅₁D₄ = C₇×C₆.D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₄₂	168		C42.51D4	336,89
C₄₂.₅₂D₄ = C₂²⋊C₄×C₂₁	central extension (φ=1)	168		C42.52D4	336,107
C₄₂.₅₃D₄ = C₄⋊C₄×C₂₁	central extension (φ=1)	336		C42.53D4	336,108
C₄₂.₅₄D₄ = D₈×C₂₁	central extension (φ=1)	168	2	C42.54D4	336,111
C₄₂.₅₅D₄ = SD₁₆×C₂₁	central extension (φ=1)	168	2	C42.55D4	336,112
C₄₂.₅₆D₄ = Q₁₆×C₂₁	central extension (φ=1)	336	2	C42.56D4	336,113

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Extensions 1→N→G→Q→1 with N=C42 and Q=D4

Extensions 1→N→G→Q→1 with N=C₄₂ and Q=D₄