Extensions 1→N→G→Q→1 with N=C₇⋊C₈ and Q=C₂³

Direct product G=N×Q with N=C₇⋊C₈ and Q=C₂³

		d	ρ	Label	ID
C₂³×C₇⋊C₈		448		C2^3xC7:C8	448,1233

Semidirect products G=N:Q with N=C₇⋊C₈ and Q=C₂³

extension	φ:Q→Out N	d	ρ	Label	ID
C₇⋊C₈⋊₁C₂³ = C₂×D₈⋊D₇	φ: C₂³/C₂ → C₂² ⊆ Out C₇⋊C₈	112		C7:C8:1C2^3	448,1208
C₇⋊C₈⋊₂C₂³ = C₂×D₅₆⋊C₂	φ: C₂³/C₂ → C₂² ⊆ Out C₇⋊C₈	112		C7:C8:2C2^3	448,1212
C₇⋊C₈⋊₃C₂³ = D₇×C₈⋊C₂²	φ: C₂³/C₂ → C₂² ⊆ Out C₇⋊C₈	56	8+	C7:C8:3C2^3	448,1225
C₇⋊C₈⋊₄C₂³ = C₂×D₄.D₁₄	φ: C₂³/C₂ → C₂² ⊆ Out C₇⋊C₈	112		C7:C8:4C2^3	448,1246
C₇⋊C₈⋊₅C₂³ = C₂×D₄⋊D₁₄	φ: C₂³/C₂ → C₂² ⊆ Out C₇⋊C₈	112		C7:C8:5C2^3	448,1273
C₇⋊C₈⋊₆C₂³ = C₂×D₇×D₈	φ: C₂³/C₂² → C₂ ⊆ Out C₇⋊C₈	112		C7:C8:6C2^3	448,1207
C₇⋊C₈⋊₇C₂³ = C₂×D₇×SD₁₆	φ: C₂³/C₂² → C₂ ⊆ Out C₇⋊C₈	112		C7:C8:7C2^3	448,1211
C₇⋊C₈⋊₈C₂³ = C₂²×D₄⋊D₇	φ: C₂³/C₂² → C₂ ⊆ Out C₇⋊C₈	224		C7:C8:8C2^3	448,1245
C₇⋊C₈⋊₉C₂³ = C₂²×D₄.D₇	φ: C₂³/C₂² → C₂ ⊆ Out C₇⋊C₈	224		C7:C8:9C2^3	448,1247
C₇⋊C₈⋊₁₀C₂³ = C₂²×Q₈⋊D₇	φ: C₂³/C₂² → C₂ ⊆ Out C₇⋊C₈	224		C7:C8:10C2^3	448,1260
C₇⋊C₈⋊₁₁C₂³ = C₂²×C₈⋊D₇	φ: C₂³/C₂² → C₂ ⊆ Out C₇⋊C₈	224		C7:C8:11C2^3	448,1190
C₇⋊C₈⋊₁₂C₂³ = C₂×D₇×M₄(2)	φ: C₂³/C₂² → C₂ ⊆ Out C₇⋊C₈	112		C7:C8:12C2^3	448,1196
C₇⋊C₈⋊₁₃C₂³ = C₂²×C₄.Dic₇	φ: C₂³/C₂² → C₂ ⊆ Out C₇⋊C₈	224		C7:C8:13C2^3	448,1234
C₇⋊C₈⋊₁₄C₂³ = D₇×C₂²×C₈	φ: trivial image	224		C7:C8:14C2^3	448,1189

Non-split extensions G=N.Q with N=C₇⋊C₈ and Q=C₂³

extension	φ:Q→Out N	d	ρ	Label	ID
C₇⋊C₈.₁C₂³ = D₈⋊₁₃D₁₄	φ: C₂³/C₂ → C₂² ⊆ Out C₇⋊C₈	112	4	C7:C8.1C2^3	448,1210
C₇⋊C₈.₂C₂³ = C₂×SD₁₆⋊D₇	φ: C₂³/C₂ → C₂² ⊆ Out C₇⋊C₈	224		C7:C8.2C2^3	448,1213
C₇⋊C₈.₃C₂³ = D₂₈.₂₉D₄	φ: C₂³/C₂ → C₂² ⊆ Out C₇⋊C₈	112	4	C7:C8.3C2^3	448,1215
C₇⋊C₈.₄C₂³ = C₂×Q₁₆⋊D₇	φ: C₂³/C₂ → C₂² ⊆ Out C₇⋊C₈	224		C7:C8.4C2^3	448,1217
C₇⋊C₈.₅C₂³ = D₂₈.₃₀D₄	φ: C₂³/C₂ → C₂² ⊆ Out C₇⋊C₈	224	4	C7:C8.5C2^3	448,1219
C₇⋊C₈.₆C₂³ = D₈⋊₁₀D₁₄	φ: C₂³/C₂ → C₂² ⊆ Out C₇⋊C₈	112	4	C7:C8.6C2^3	448,1221
C₇⋊C₈.₇C₂³ = D₈⋊₁₅D₁₄	φ: C₂³/C₂ → C₂² ⊆ Out C₇⋊C₈	112	4+	C7:C8.7C2^3	448,1222
C₇⋊C₈.₈C₂³ = D₈⋊₁₁D₁₄	φ: C₂³/C₂ → C₂² ⊆ Out C₇⋊C₈	112	4	C7:C8.8C2^3	448,1223
C₇⋊C₈.₉C₂³ = D₈.₁₀D₁₄	φ: C₂³/C₂ → C₂² ⊆ Out C₇⋊C₈	224	4-	C7:C8.9C2^3	448,1224
C₇⋊C₈.₁₀C₂³ = SD₁₆⋊D₁₄	φ: C₂³/C₂ → C₂² ⊆ Out C₇⋊C₈	112	8-	C7:C8.10C2^3	448,1226
C₇⋊C₈.₁₁C₂³ = D₇×C₈.C₂²	φ: C₂³/C₂ → C₂² ⊆ Out C₇⋊C₈	112	8-	C7:C8.11C2^3	448,1229
C₇⋊C₈.₁₂C₂³ = D₅₆⋊C₂²	φ: C₂³/C₂ → C₂² ⊆ Out C₇⋊C₈	112	8+	C7:C8.12C2^3	448,1230
C₇⋊C₈.₁₃C₂³ = C₂×C₂₈.C₂³	φ: C₂³/C₂ → C₂² ⊆ Out C₇⋊C₈	224		C7:C8.13C2^3	448,1261
C₇⋊C₈.₁₄C₂³ = C₂₈.C₂⁴	φ: C₂³/C₂ → C₂² ⊆ Out C₇⋊C₈	112	4	C7:C8.14C2^3	448,1275
C₇⋊C₈.₁₅C₂³ = C₂×D₄.₉D₁₄	φ: C₂³/C₂ → C₂² ⊆ Out C₇⋊C₈	224		C7:C8.15C2^3	448,1276
C₇⋊C₈.₁₆C₂³ = D₂₈.₃₂C₂³	φ: C₂³/C₂ → C₂² ⊆ Out C₇⋊C₈	112	8+	C7:C8.16C2^3	448,1288
C₇⋊C₈.₁₇C₂³ = D₂₈.₃₃C₂³	φ: C₂³/C₂ → C₂² ⊆ Out C₇⋊C₈	112	8-	C7:C8.17C2^3	448,1289
C₇⋊C₈.₁₈C₂³ = D₂₈.₃₄C₂³	φ: C₂³/C₂ → C₂² ⊆ Out C₇⋊C₈	112	8+	C7:C8.18C2^3	448,1290
C₇⋊C₈.₁₉C₂³ = D₂₈.₃₅C₂³	φ: C₂³/C₂ → C₂² ⊆ Out C₇⋊C₈	224	8-	C7:C8.19C2^3	448,1291
C₇⋊C₈.₂₀C₂³ = C₂×D₈⋊₃D₇	φ: C₂³/C₂² → C₂ ⊆ Out C₇⋊C₈	224		C7:C8.20C2^3	448,1209
C₇⋊C₈.₂₁C₂³ = C₂×SD₁₆⋊₃D₇	φ: C₂³/C₂² → C₂ ⊆ Out C₇⋊C₈	224		C7:C8.21C2^3	448,1214
C₇⋊C₈.₂₂C₂³ = C₂×D₇×Q₁₆	φ: C₂³/C₂² → C₂ ⊆ Out C₇⋊C₈	224		C7:C8.22C2^3	448,1216
C₇⋊C₈.₂₃C₂³ = C₂×Q₈.D₁₄	φ: C₂³/C₂² → C₂ ⊆ Out C₇⋊C₈	224		C7:C8.23C2^3	448,1218
C₇⋊C₈.₂₄C₂³ = D₇×C₄○D₈	φ: C₂³/C₂² → C₂ ⊆ Out C₇⋊C₈	112	4	C7:C8.24C2^3	448,1220
C₇⋊C₈.₂₅C₂³ = D₈⋊₅D₁₄	φ: C₂³/C₂² → C₂ ⊆ Out C₇⋊C₈	112	8+	C7:C8.25C2^3	448,1227
C₇⋊C₈.₂₆C₂³ = D₈⋊₆D₁₄	φ: C₂³/C₂² → C₂ ⊆ Out C₇⋊C₈	112	8-	C7:C8.26C2^3	448,1228
C₇⋊C₈.₂₇C₂³ = C₅₆.C₂³	φ: C₂³/C₂² → C₂ ⊆ Out C₇⋊C₈	112	8+	C7:C8.27C2^3	448,1231
C₇⋊C₈.₂₈C₂³ = D₂₈.₄₄D₄	φ: C₂³/C₂² → C₂ ⊆ Out C₇⋊C₈	224	8-	C7:C8.28C2^3	448,1232
C₇⋊C₈.₂₉C₂³ = C₂²×C₇⋊Q₁₆	φ: C₂³/C₂² → C₂ ⊆ Out C₇⋊C₈	448		C7:C8.29C2^3	448,1262
C₇⋊C₈.₃₀C₂³ = C₂×D₄.₈D₁₄	φ: C₂³/C₂² → C₂ ⊆ Out C₇⋊C₈	224		C7:C8.30C2^3	448,1274
C₇⋊C₈.₃₁C₂³ = C₂×D₂₈.₂C₄	φ: C₂³/C₂² → C₂ ⊆ Out C₇⋊C₈	224		C7:C8.31C2^3	448,1191
C₇⋊C₈.₃₂C₂³ = C₂₈.₇₀C₂⁴	φ: C₂³/C₂² → C₂ ⊆ Out C₇⋊C₈	112	4	C7:C8.32C2^3	448,1198
C₇⋊C₈.₃₃C₂³ = C₅₆.₄₉C₂³	φ: C₂³/C₂² → C₂ ⊆ Out C₇⋊C₈	112	4	C7:C8.33C2^3	448,1203
C₇⋊C₈.₃₄C₂³ = C₂₈.₇₆C₂⁴	φ: C₂³/C₂² → C₂ ⊆ Out C₇⋊C₈	112	4	C7:C8.34C2^3	448,1272
C₇⋊C₈.₃₅C₂³ = C₂×D₂₈.C₄	φ: trivial image	224		C7:C8.35C2^3	448,1197
C₇⋊C₈.₃₆C₂³ = D₇×C₈○D₄	φ: trivial image	112	4	C7:C8.36C2^3	448,1202
C₇⋊C₈.₃₇C₂³ = C₂×Q₈.Dic₇	φ: trivial image	224		C7:C8.37C2^3	448,1271

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Extensions 1→N→G→Q→1 with N=C7⋊C8 and Q=C23

Extensions 1→N→G→Q→1 with N=C₇⋊C₈ and Q=C₂³