Extensions 1→N→G→Q→1 with N=C₂₈ and Q=C₂³

Direct product G=N×Q with N=C₂₈ and Q=C₂³

		d	ρ	Label	ID
C₂³×C₂₈		224		C2^3xC28	224,189

Semidirect products G=N:Q with N=C₂₈ and Q=C₂³

extension	φ:Q→Aut N	d	Label	ID
C₂₈⋊C₂³ = C₂×D₄×D₇	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₈	56	C28:C2^3	224,178
C₂₈⋊₂C₂³ = C₂²×D₂₈	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₈	112	C28:2C2^3	224,176
C₂₈⋊₃C₂³ = D₇×C₂²×C₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₈	112	C28:3C2^3	224,175
C₂₈⋊₄C₂³ = D₄×C₂×C₁₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₈	112	C28:4C2^3	224,190

Non-split extensions G=N.Q with N=C₂₈ and Q=C₂³

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₈.₁C₂³ = D₇×D₈	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₈	56	4+	C28.1C2^3	224,105
C₂₈.₂C₂³ = D₈⋊D₇	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₈	56	4	C28.2C2^3	224,106
C₂₈.₃C₂³ = D₈⋊₃D₇	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₈	112	4-	C28.3C2^3	224,107
C₂₈.₄C₂³ = D₇×SD₁₆	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₈	56	4	C28.4C2^3	224,108
C₂₈.₅C₂³ = D₅₆⋊C₂	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₈	56	4+	C28.5C2^3	224,109
C₂₈.₆C₂³ = SD₁₆⋊D₇	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₈	112	4-	C28.6C2^3	224,110
C₂₈.₇C₂³ = SD₁₆⋊₃D₇	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₈	112	4	C28.7C2^3	224,111
C₂₈.₈C₂³ = D₇×Q₁₆	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₈	112	4-	C28.8C2^3	224,112
C₂₈.₉C₂³ = Q₁₆⋊D₇	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₈	112	4	C28.9C2^3	224,113
C₂₈.₁₀C₂³ = Q₈.D₁₄	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₈	112	4+	C28.10C2^3	224,114
C₂₈.₁₁C₂³ = C₂×D₄⋊D₇	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₈	112		C28.11C2^3	224,126
C₂₈.₁₂C₂³ = D₄.D₁₄	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₈	56	4	C28.12C2^3	224,127
C₂₈.₁₃C₂³ = C₂×D₄.D₇	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₈	112		C28.13C2^3	224,128
C₂₈.₁₄C₂³ = C₂×Q₈⋊D₇	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₈	112		C28.14C2^3	224,136
C₂₈.₁₅C₂³ = C₂₈.C₂³	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₈	112	4	C28.15C2^3	224,137
C₂₈.₁₆C₂³ = C₂×C₇⋊Q₁₆	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₈	224		C28.16C2^3	224,138
C₂₈.₁₇C₂³ = D₄⋊D₁₄	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₈	56	4+	C28.17C2^3	224,144
C₂₈.₁₈C₂³ = D₄.₈D₁₄	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₈	112	4	C28.18C2^3	224,145
C₂₈.₁₉C₂³ = D₄.₉D₁₄	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₈	112	4-	C28.19C2^3	224,146
C₂₈.₂₀C₂³ = C₂×D₄⋊₂D₇	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₈	112		C28.20C2^3	224,179
C₂₈.₂₁C₂³ = D₄⋊₆D₁₄	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₈	56	4	C28.21C2^3	224,180
C₂₈.₂₂C₂³ = C₂×Q₈×D₇	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₈	112		C28.22C2^3	224,181
C₂₈.₂₃C₂³ = C₂×Q₈⋊₂D₇	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₈	112		C28.23C2^3	224,182
C₂₈.₂₄C₂³ = Q₈.₁₀D₁₄	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₈	112	4	C28.24C2^3	224,183
C₂₈.₂₅C₂³ = D₇×C₄○D₄	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₈	56	4	C28.25C2^3	224,184
C₂₈.₂₆C₂³ = D₄⋊₈D₁₄	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₈	56	4+	C28.26C2^3	224,185
C₂₈.₂₇C₂³ = D₄.₁₀D₁₄	φ: C₂³/C₂ → C₂² ⊆ Aut C₂₈	112	4-	C28.27C2^3	224,186
C₂₈.₂₈C₂³ = C₂×C₅₆⋊C₂	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₈	112		C28.28C2^3	224,97
C₂₈.₂₉C₂³ = C₂×D₅₆	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₈	112		C28.29C2^3	224,98
C₂₈.₃₀C₂³ = D₅₆⋊₇C₂	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₈	112	2	C28.30C2^3	224,99
C₂₈.₃₁C₂³ = C₂×Dic₂₈	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₈	224		C28.31C2^3	224,100
C₂₈.₃₂C₂³ = C₈⋊D₁₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₈	56	4+	C28.32C2^3	224,103
C₂₈.₃₃C₂³ = C₈.D₁₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₈	112	4-	C28.33C2^3	224,104
C₂₈.₃₄C₂³ = C₂²×Dic₁₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₈	224		C28.34C2^3	224,174
C₂₈.₃₅C₂³ = D₇×C₂×C₈	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₈	112		C28.35C2^3	224,94
C₂₈.₃₆C₂³ = C₂×C₈⋊D₇	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₈	112		C28.36C2^3	224,95
C₂₈.₃₇C₂³ = D₂₈.₂C₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₈	112	2	C28.37C2^3	224,96
C₂₈.₃₈C₂³ = D₇×M₄(2)	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₈	56	4	C28.38C2^3	224,101
C₂₈.₃₉C₂³ = D₂₈.C₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₈	112	4	C28.39C2^3	224,102
C₂₈.₄₀C₂³ = C₂²×C₇⋊C₈	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₈	224		C28.40C2^3	224,115
C₂₈.₄₁C₂³ = C₂×C₄.Dic₇	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₈	112		C28.41C2^3	224,116
C₂₈.₄₂C₂³ = Q₈.Dic₇	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₈	112	4	C28.42C2^3	224,143
C₂₈.₄₃C₂³ = C₂×C₄○D₂₈	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₈	112		C28.43C2^3	224,177
C₂₈.₄₄C₂³ = C₁₄×D₈	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₈	112		C28.44C2^3	224,167
C₂₈.₄₅C₂³ = C₁₄×SD₁₆	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₈	112		C28.45C2^3	224,168
C₂₈.₄₆C₂³ = C₁₄×Q₁₆	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₈	224		C28.46C2^3	224,169
C₂₈.₄₇C₂³ = C₇×C₄○D₈	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₈	112	2	C28.47C2^3	224,170
C₂₈.₄₈C₂³ = C₇×C₈⋊C₂²	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₈	56	4	C28.48C2^3	224,171
C₂₈.₄₉C₂³ = C₇×C₈.C₂²	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₈	112	4	C28.49C2^3	224,172
C₂₈.₅₀C₂³ = Q₈×C₂×C₁₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₈	224		C28.50C2^3	224,191
C₂₈.₅₁C₂³ = C₇×2₊¹⁺⁴	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₈	56	4	C28.51C2^3	224,193
C₂₈.₅₂C₂³ = C₇×2_-¹⁺⁴	φ: C₂³/C₂² → C₂ ⊆ Aut C₂₈	112	4	C28.52C2^3	224,194
C₂₈.₅₃C₂³ = C₁₄×M₄(2)	central extension (φ=1)	112		C28.53C2^3	224,165
C₂₈.₅₄C₂³ = C₇×C₈○D₄	central extension (φ=1)	112	2	C28.54C2^3	224,166
C₂₈.₅₅C₂³ = C₁₄×C₄○D₄	central extension (φ=1)	112		C28.55C2^3	224,192

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Extensions 1→N→G→Q→1 with N=C28 and Q=C23

Extensions 1→N→G→Q→1 with N=C₂₈ and Q=C₂³