Extensions 1→N→G→Q→1 with N=C₄₂ and Q=C₂³

Direct product G=N×Q with N=C₄₂ and Q=C₂³

		d	ρ	Label	ID
C₂³×C₄₂		336		C2^3xC42	336,228

Semidirect products G=N:Q with N=C₄₂ and Q=C₂³

extension	φ:Q→Aut N	d	Label	ID
C₄₂⋊C₂³ = C₂²×S₃×D₇	φ: C₂³/C₂ → C₂² ⊆ Aut C₄₂	84	C42:C2^3	336,219
C₄₂⋊₂C₂³ = C₂³×D₂₁	φ: C₂³/C₂² → C₂ ⊆ Aut C₄₂	168	C42:2C2^3	336,227
C₄₂⋊₃C₂³ = D₇×C₂²×C₆	φ: C₂³/C₂² → C₂ ⊆ Aut C₄₂	168	C42:3C2^3	336,225
C₄₂⋊₄C₂³ = S₃×C₂²×C₁₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₄₂	168	C42:4C2^3	336,226

Non-split extensions G=N.Q with N=C₄₂ and Q=C₂³

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄₂.₁C₂³ = D₇×Dic₆	φ: C₂³/C₂ → C₂² ⊆ Aut C₄₂	168	4-	C42.1C2^3	336,137
C₄₂.₂C₂³ = D₂₈⋊₅S₃	φ: C₂³/C₂ → C₂² ⊆ Aut C₄₂	168	4-	C42.2C2^3	336,138
C₄₂.₃C₂³ = D₂₈⋊S₃	φ: C₂³/C₂ → C₂² ⊆ Aut C₄₂	168	4	C42.3C2^3	336,139
C₄₂.₄C₂³ = S₃×Dic₁₄	φ: C₂³/C₂ → C₂² ⊆ Aut C₄₂	168	4-	C42.4C2^3	336,140
C₄₂.₅C₂³ = D₁₂⋊D₇	φ: C₂³/C₂ → C₂² ⊆ Aut C₄₂	168	4	C42.5C2^3	336,141
C₄₂.₆C₂³ = D₈₄⋊C₂	φ: C₂³/C₂ → C₂² ⊆ Aut C₄₂	168	4+	C42.6C2^3	336,142
C₄₂.₇C₂³ = D₂₁⋊Q₈	φ: C₂³/C₂ → C₂² ⊆ Aut C₄₂	168	4	C42.7C2^3	336,143
C₄₂.₈C₂³ = D₆.D₁₄	φ: C₂³/C₂ → C₂² ⊆ Aut C₄₂	168	4	C42.8C2^3	336,144
C₄₂.₉C₂³ = D₁₂⋊₅D₇	φ: C₂³/C₂ → C₂² ⊆ Aut C₄₂	168	4-	C42.9C2^3	336,145
C₄₂.₁₀C₂³ = D₁₄.D₆	φ: C₂³/C₂ → C₂² ⊆ Aut C₄₂	168	4+	C42.10C2^3	336,146
C₄₂.₁₁C₂³ = C₄×S₃×D₇	φ: C₂³/C₂ → C₂² ⊆ Aut C₄₂	84	4	C42.11C2^3	336,147
C₄₂.₁₂C₂³ = D₇×D₁₂	φ: C₂³/C₂ → C₂² ⊆ Aut C₄₂	84	4+	C42.12C2^3	336,148
C₄₂.₁₃C₂³ = S₃×D₂₈	φ: C₂³/C₂ → C₂² ⊆ Aut C₄₂	84	4+	C42.13C2^3	336,149
C₄₂.₁₄C₂³ = C₂₈⋊D₆	φ: C₂³/C₂ → C₂² ⊆ Aut C₄₂	84	4	C42.14C2^3	336,150
C₄₂.₁₅C₂³ = C₂×Dic₃×D₇	φ: C₂³/C₂ → C₂² ⊆ Aut C₄₂	168		C42.15C2^3	336,151
C₄₂.₁₆C₂³ = Dic₇.D₆	φ: C₂³/C₂ → C₂² ⊆ Aut C₄₂	168	4	C42.16C2^3	336,152
C₄₂.₁₇C₂³ = C₄₂.C₂³	φ: C₂³/C₂ → C₂² ⊆ Aut C₄₂	168	4-	C42.17C2^3	336,153
C₄₂.₁₈C₂³ = C₂×S₃×Dic₇	φ: C₂³/C₂ → C₂² ⊆ Aut C₄₂	168		C42.18C2^3	336,154
C₄₂.₁₉C₂³ = Dic₃.D₁₄	φ: C₂³/C₂ → C₂² ⊆ Aut C₄₂	168	4	C42.19C2^3	336,155
C₄₂.₂₀C₂³ = C₂×D₂₁⋊C₄	φ: C₂³/C₂ → C₂² ⊆ Aut C₄₂	168		C42.20C2^3	336,156
C₄₂.₂₁C₂³ = C₂×C₂₁⋊D₄	φ: C₂³/C₂ → C₂² ⊆ Aut C₄₂	168		C42.21C2^3	336,157
C₄₂.₂₂C₂³ = C₂×C₃⋊D₂₈	φ: C₂³/C₂ → C₂² ⊆ Aut C₄₂	168		C42.22C2^3	336,158
C₄₂.₂₃C₂³ = C₂×C₇⋊D₁₂	φ: C₂³/C₂ → C₂² ⊆ Aut C₄₂	168		C42.23C2^3	336,159
C₄₂.₂₄C₂³ = C₂×C₂₁⋊Q₈	φ: C₂³/C₂ → C₂² ⊆ Aut C₄₂	336		C42.24C2^3	336,160
C₄₂.₂₅C₂³ = D₇×C₃⋊D₄	φ: C₂³/C₂ → C₂² ⊆ Aut C₄₂	84	4	C42.25C2^3	336,161
C₄₂.₂₆C₂³ = S₃×C₇⋊D₄	φ: C₂³/C₂ → C₂² ⊆ Aut C₄₂	84	4	C42.26C2^3	336,162
C₄₂.₂₇C₂³ = D₆⋊D₁₄	φ: C₂³/C₂ → C₂² ⊆ Aut C₄₂	84	4+	C42.27C2^3	336,163
C₄₂.₂₈C₂³ = C₂×Dic₄₂	φ: C₂³/C₂² → C₂ ⊆ Aut C₄₂	336		C42.28C2^3	336,194
C₄₂.₂₉C₂³ = C₂×C₄×D₂₁	φ: C₂³/C₂² → C₂ ⊆ Aut C₄₂	168		C42.29C2^3	336,195
C₄₂.₃₀C₂³ = C₂×D₈₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₄₂	168		C42.30C2^3	336,196
C₄₂.₃₁C₂³ = D₈₄⋊₁₁C₂	φ: C₂³/C₂² → C₂ ⊆ Aut C₄₂	168	2	C42.31C2^3	336,197
C₄₂.₃₂C₂³ = D₄×D₂₁	φ: C₂³/C₂² → C₂ ⊆ Aut C₄₂	84	4+	C42.32C2^3	336,198
C₄₂.₃₃C₂³ = D₄⋊₂D₂₁	φ: C₂³/C₂² → C₂ ⊆ Aut C₄₂	168	4-	C42.33C2^3	336,199
C₄₂.₃₄C₂³ = Q₈×D₂₁	φ: C₂³/C₂² → C₂ ⊆ Aut C₄₂	168	4-	C42.34C2^3	336,200
C₄₂.₃₅C₂³ = Q₈⋊₃D₂₁	φ: C₂³/C₂² → C₂ ⊆ Aut C₄₂	168	4+	C42.35C2^3	336,201
C₄₂.₃₆C₂³ = C₂²×Dic₂₁	φ: C₂³/C₂² → C₂ ⊆ Aut C₄₂	336		C42.36C2^3	336,202
C₄₂.₃₇C₂³ = C₂×C₂₁⋊₇D₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₄₂	168		C42.37C2^3	336,203
C₄₂.₃₈C₂³ = C₆×Dic₁₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₄₂	336		C42.38C2^3	336,174
C₄₂.₃₉C₂³ = D₇×C₂×C₁₂	φ: C₂³/C₂² → C₂ ⊆ Aut C₄₂	168		C42.39C2^3	336,175
C₄₂.₄₀C₂³ = C₆×D₂₈	φ: C₂³/C₂² → C₂ ⊆ Aut C₄₂	168		C42.40C2^3	336,176
C₄₂.₄₁C₂³ = C₃×C₄○D₂₈	φ: C₂³/C₂² → C₂ ⊆ Aut C₄₂	168	2	C42.41C2^3	336,177
C₄₂.₄₂C₂³ = C₃×D₄×D₇	φ: C₂³/C₂² → C₂ ⊆ Aut C₄₂	84	4	C42.42C2^3	336,178
C₄₂.₄₃C₂³ = C₃×D₄⋊₂D₇	φ: C₂³/C₂² → C₂ ⊆ Aut C₄₂	168	4	C42.43C2^3	336,179
C₄₂.₄₄C₂³ = C₃×Q₈×D₇	φ: C₂³/C₂² → C₂ ⊆ Aut C₄₂	168	4	C42.44C2^3	336,180
C₄₂.₄₅C₂³ = C₃×Q₈⋊₂D₇	φ: C₂³/C₂² → C₂ ⊆ Aut C₄₂	168	4	C42.45C2^3	336,181
C₄₂.₄₆C₂³ = C₂×C₆×Dic₇	φ: C₂³/C₂² → C₂ ⊆ Aut C₄₂	336		C42.46C2^3	336,182
C₄₂.₄₇C₂³ = C₆×C₇⋊D₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₄₂	168		C42.47C2^3	336,183
C₄₂.₄₈C₂³ = C₁₄×Dic₆	φ: C₂³/C₂² → C₂ ⊆ Aut C₄₂	336		C42.48C2^3	336,184
C₄₂.₄₉C₂³ = S₃×C₂×C₂₈	φ: C₂³/C₂² → C₂ ⊆ Aut C₄₂	168		C42.49C2^3	336,185
C₄₂.₅₀C₂³ = C₁₄×D₁₂	φ: C₂³/C₂² → C₂ ⊆ Aut C₄₂	168		C42.50C2^3	336,186
C₄₂.₅₁C₂³ = C₇×C₄○D₁₂	φ: C₂³/C₂² → C₂ ⊆ Aut C₄₂	168	2	C42.51C2^3	336,187
C₄₂.₅₂C₂³ = S₃×C₇×D₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₄₂	84	4	C42.52C2^3	336,188
C₄₂.₅₃C₂³ = C₇×D₄⋊₂S₃	φ: C₂³/C₂² → C₂ ⊆ Aut C₄₂	168	4	C42.53C2^3	336,189
C₄₂.₅₄C₂³ = S₃×C₇×Q₈	φ: C₂³/C₂² → C₂ ⊆ Aut C₄₂	168	4	C42.54C2^3	336,190
C₄₂.₅₅C₂³ = C₇×Q₈⋊₃S₃	φ: C₂³/C₂² → C₂ ⊆ Aut C₄₂	168	4	C42.55C2^3	336,191
C₄₂.₅₆C₂³ = Dic₃×C₂×C₁₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₄₂	336		C42.56C2^3	336,192
C₄₂.₅₇C₂³ = C₁₄×C₃⋊D₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₄₂	168		C42.57C2^3	336,193
C₄₂.₅₈C₂³ = D₄×C₄₂	central extension (φ=1)	168		C42.58C2^3	336,205
C₄₂.₅₉C₂³ = Q₈×C₄₂	central extension (φ=1)	336		C42.59C2^3	336,206
C₄₂.₆₀C₂³ = C₄○D₄×C₂₁	central extension (φ=1)	168	2	C42.60C2^3	336,207

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C42 and Q=C23

Extensions 1→N→G→Q→1 with N=C₄₂ and Q=C₂³