Extensions 1→N→G→Q→1 with N=C₄ and Q=C₂³×D₇

Direct product G=N×Q with N=C₄ and Q=C₂³×D₇

		d	ρ	Label	ID
D₇×C₂³×C₄		224		D7xC2^3xC4	448,1366

Semidirect products G=N:Q with N=C₄ and Q=C₂³×D₇

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊₁(C₂³×D₇) = C₂²×D₄×D₇	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	112		C4:1(C2^3xD7)	448,1369
C₄⋊₂(C₂³×D₇) = C₂³×D₂₈	φ: C₂³×D₇/C₂²×C₁₄ → C₂ ⊆ Aut C₄	224		C4:2(C2^3xD7)	448,1367

Non-split extensions G=N.Q with N=C₄ and Q=C₂³×D₇

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁(C₂³×D₇) = C₂×D₇×D₈	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	112		C4.1(C2^3xD7)	448,1207
C₄.₂(C₂³×D₇) = C₂×D₈⋊D₇	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	112		C4.2(C2^3xD7)	448,1208
C₄.₃(C₂³×D₇) = C₂×D₈⋊₃D₇	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	224		C4.3(C2^3xD7)	448,1209
C₄.₄(C₂³×D₇) = D₈⋊₁₃D₁₄	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	112	4	C4.4(C2^3xD7)	448,1210
C₄.₅(C₂³×D₇) = C₂×D₇×SD₁₆	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	112		C4.5(C2^3xD7)	448,1211
C₄.₆(C₂³×D₇) = C₂×D₅₆⋊C₂	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	112		C4.6(C2^3xD7)	448,1212
C₄.₇(C₂³×D₇) = C₂×SD₁₆⋊D₇	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	224		C4.7(C2^3xD7)	448,1213
C₄.₈(C₂³×D₇) = C₂×SD₁₆⋊₃D₇	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	224		C4.8(C2^3xD7)	448,1214
C₄.₉(C₂³×D₇) = D₂₈.₂₉D₄	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	112	4	C4.9(C2^3xD7)	448,1215
C₄.₁₀(C₂³×D₇) = C₂×D₇×Q₁₆	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	224		C4.10(C2^3xD7)	448,1216
C₄.₁₁(C₂³×D₇) = C₂×Q₁₆⋊D₇	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	224		C4.11(C2^3xD7)	448,1217
C₄.₁₂(C₂³×D₇) = C₂×Q₈.D₁₄	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	224		C4.12(C2^3xD7)	448,1218
C₄.₁₃(C₂³×D₇) = D₂₈.₃₀D₄	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	224	4	C4.13(C2^3xD7)	448,1219
C₄.₁₄(C₂³×D₇) = D₇×C₄○D₈	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	112	4	C4.14(C2^3xD7)	448,1220
C₄.₁₅(C₂³×D₇) = D₈⋊₁₀D₁₄	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	112	4	C4.15(C2^3xD7)	448,1221
C₄.₁₆(C₂³×D₇) = D₈⋊₁₅D₁₄	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	112	4+	C4.16(C2^3xD7)	448,1222
C₄.₁₇(C₂³×D₇) = D₈⋊₁₁D₁₄	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	112	4	C4.17(C2^3xD7)	448,1223
C₄.₁₈(C₂³×D₇) = D₈.₁₀D₁₄	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	224	4-	C4.18(C2^3xD7)	448,1224
C₄.₁₉(C₂³×D₇) = D₇×C₈⋊C₂²	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	56	8+	C4.19(C2^3xD7)	448,1225
C₄.₂₀(C₂³×D₇) = SD₁₆⋊D₁₄	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	112	8-	C4.20(C2^3xD7)	448,1226
C₄.₂₁(C₂³×D₇) = D₈⋊₅D₁₄	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	112	8+	C4.21(C2^3xD7)	448,1227
C₄.₂₂(C₂³×D₇) = D₈⋊₆D₁₄	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	112	8-	C4.22(C2^3xD7)	448,1228
C₄.₂₃(C₂³×D₇) = D₇×C₈.C₂²	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	112	8-	C4.23(C2^3xD7)	448,1229
C₄.₂₄(C₂³×D₇) = D₅₆⋊C₂²	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	112	8+	C4.24(C2^3xD7)	448,1230
C₄.₂₅(C₂³×D₇) = C₅₆.C₂³	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	112	8+	C4.25(C2^3xD7)	448,1231
C₄.₂₆(C₂³×D₇) = D₂₈.₄₄D₄	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	224	8-	C4.26(C2^3xD7)	448,1232
C₄.₂₇(C₂³×D₇) = C₂²×D₄⋊D₇	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	224		C4.27(C2^3xD7)	448,1245
C₄.₂₈(C₂³×D₇) = C₂×D₄.D₁₄	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	112		C4.28(C2^3xD7)	448,1246
C₄.₂₉(C₂³×D₇) = C₂²×D₄.D₇	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	224		C4.29(C2^3xD7)	448,1247
C₄.₃₀(C₂³×D₇) = C₂²×Q₈⋊D₇	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	224		C4.30(C2^3xD7)	448,1260
C₄.₃₁(C₂³×D₇) = C₂×C₂₈.C₂³	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	224		C4.31(C2^3xD7)	448,1261
C₄.₃₂(C₂³×D₇) = C₂²×C₇⋊Q₁₆	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	448		C4.32(C2^3xD7)	448,1262
C₄.₃₃(C₂³×D₇) = C₂×D₄⋊D₁₄	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	112		C4.33(C2^3xD7)	448,1273
C₄.₃₄(C₂³×D₇) = C₂×D₄.₈D₁₄	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	224		C4.34(C2^3xD7)	448,1274
C₄.₃₅(C₂³×D₇) = C₂₈.C₂⁴	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	112	4	C4.35(C2^3xD7)	448,1275
C₄.₃₆(C₂³×D₇) = C₂×D₄.₉D₁₄	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	224		C4.36(C2^3xD7)	448,1276
C₄.₃₇(C₂³×D₇) = D₂₈.₃₂C₂³	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	112	8+	C4.37(C2^3xD7)	448,1288
C₄.₃₈(C₂³×D₇) = D₂₈.₃₃C₂³	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	112	8-	C4.38(C2^3xD7)	448,1289
C₄.₃₉(C₂³×D₇) = D₂₈.₃₄C₂³	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	112	8+	C4.39(C2^3xD7)	448,1290
C₄.₄₀(C₂³×D₇) = D₂₈.₃₅C₂³	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	224	8-	C4.40(C2^3xD7)	448,1291
C₄.₄₁(C₂³×D₇) = C₂²×D₄⋊₂D₇	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	224		C4.41(C2^3xD7)	448,1370
C₄.₄₂(C₂³×D₇) = C₂×D₄⋊₆D₁₄	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	112		C4.42(C2^3xD7)	448,1371
C₄.₄₃(C₂³×D₇) = C₂²×Q₈×D₇	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	224		C4.43(C2^3xD7)	448,1372
C₄.₄₄(C₂³×D₇) = C₂²×Q₈⋊₂D₇	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	224		C4.44(C2^3xD7)	448,1373
C₄.₄₅(C₂³×D₇) = C₂×Q₈.₁₀D₁₄	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	224		C4.45(C2^3xD7)	448,1374
C₄.₄₆(C₂³×D₇) = C₁₄.C₂⁵	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	112	4	C4.46(C2^3xD7)	448,1378
C₄.₄₇(C₂³×D₇) = D₇×2₊¹⁺⁴	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	56	8+	C4.47(C2^3xD7)	448,1379
C₄.₄₈(C₂³×D₇) = D₁₄.C₂⁴	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	112	8-	C4.48(C2^3xD7)	448,1380
C₄.₄₉(C₂³×D₇) = D₇×2_-¹⁺⁴	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	112	8-	C4.49(C2^3xD7)	448,1381
C₄.₅₀(C₂³×D₇) = D₂₈.₃₉C₂³	φ: C₂³×D₇/C₂²×D₇ → C₂ ⊆ Aut C₄	112	8+	C4.50(C2^3xD7)	448,1382
C₄.₅₁(C₂³×D₇) = C₂²×C₅₆⋊C₂	φ: C₂³×D₇/C₂²×C₁₄ → C₂ ⊆ Aut C₄	224		C4.51(C2^3xD7)	448,1192
C₄.₅₂(C₂³×D₇) = C₂²×D₅₆	φ: C₂³×D₇/C₂²×C₁₄ → C₂ ⊆ Aut C₄	224		C4.52(C2^3xD7)	448,1193
C₄.₅₃(C₂³×D₇) = C₂×D₅₆⋊₇C₂	φ: C₂³×D₇/C₂²×C₁₄ → C₂ ⊆ Aut C₄	224		C4.53(C2^3xD7)	448,1194
C₄.₅₄(C₂³×D₇) = C₂²×Dic₂₈	φ: C₂³×D₇/C₂²×C₁₄ → C₂ ⊆ Aut C₄	448		C4.54(C2^3xD7)	448,1195
C₄.₅₅(C₂³×D₇) = C₂×C₈⋊D₁₄	φ: C₂³×D₇/C₂²×C₁₄ → C₂ ⊆ Aut C₄	112		C4.55(C2^3xD7)	448,1199
C₄.₅₆(C₂³×D₇) = C₂×C₈.D₁₄	φ: C₂³×D₇/C₂²×C₁₄ → C₂ ⊆ Aut C₄	224		C4.56(C2^3xD7)	448,1200
C₄.₅₇(C₂³×D₇) = C₅₆.₉C₂³	φ: C₂³×D₇/C₂²×C₁₄ → C₂ ⊆ Aut C₄	112	4	C4.57(C2^3xD7)	448,1201
C₄.₅₈(C₂³×D₇) = D₄.₁₁D₂₈	φ: C₂³×D₇/C₂²×C₁₄ → C₂ ⊆ Aut C₄	112	4	C4.58(C2^3xD7)	448,1204
C₄.₅₉(C₂³×D₇) = D₄.₁₂D₂₈	φ: C₂³×D₇/C₂²×C₁₄ → C₂ ⊆ Aut C₄	112	4+	C4.59(C2^3xD7)	448,1205
C₄.₆₀(C₂³×D₇) = D₄.₁₃D₂₈	φ: C₂³×D₇/C₂²×C₁₄ → C₂ ⊆ Aut C₄	224	4-	C4.60(C2^3xD7)	448,1206
C₄.₆₁(C₂³×D₇) = C₂³×Dic₁₄	φ: C₂³×D₇/C₂²×C₁₄ → C₂ ⊆ Aut C₄	448		C4.61(C2^3xD7)	448,1365
C₄.₆₂(C₂³×D₇) = C₂×D₄⋊₈D₁₄	φ: C₂³×D₇/C₂²×C₁₄ → C₂ ⊆ Aut C₄	112		C4.62(C2^3xD7)	448,1376
C₄.₆₃(C₂³×D₇) = C₂×D₄.₁₀D₁₄	φ: C₂³×D₇/C₂²×C₁₄ → C₂ ⊆ Aut C₄	224		C4.63(C2^3xD7)	448,1377
C₄.₆₄(C₂³×D₇) = D₇×C₂²×C₈	central extension (φ=1)	224		C4.64(C2^3xD7)	448,1189
C₄.₆₅(C₂³×D₇) = C₂²×C₈⋊D₇	central extension (φ=1)	224		C4.65(C2^3xD7)	448,1190
C₄.₆₆(C₂³×D₇) = C₂×D₂₈.₂C₄	central extension (φ=1)	224		C4.66(C2^3xD7)	448,1191
C₄.₆₇(C₂³×D₇) = C₂×D₇×M₄(2)	central extension (φ=1)	112		C4.67(C2^3xD7)	448,1196
C₄.₆₈(C₂³×D₇) = C₂×D₂₈.C₄	central extension (φ=1)	224		C4.68(C2^3xD7)	448,1197
C₄.₆₉(C₂³×D₇) = C₂₈.₇₀C₂⁴	central extension (φ=1)	112	4	C4.69(C2^3xD7)	448,1198
C₄.₇₀(C₂³×D₇) = D₇×C₈○D₄	central extension (φ=1)	112	4	C4.70(C2^3xD7)	448,1202
C₄.₇₁(C₂³×D₇) = C₅₆.₄₉C₂³	central extension (φ=1)	112	4	C4.71(C2^3xD7)	448,1203
C₄.₇₂(C₂³×D₇) = C₂³×C₇⋊C₈	central extension (φ=1)	448		C4.72(C2^3xD7)	448,1233
C₄.₇₃(C₂³×D₇) = C₂²×C₄.Dic₇	central extension (φ=1)	224		C4.73(C2^3xD7)	448,1234
C₄.₇₄(C₂³×D₇) = C₂×Q₈.Dic₇	central extension (φ=1)	224		C4.74(C2^3xD7)	448,1271
C₄.₇₅(C₂³×D₇) = C₂₈.₇₆C₂⁴	central extension (φ=1)	112	4	C4.75(C2^3xD7)	448,1272
C₄.₇₆(C₂³×D₇) = C₂²×C₄○D₂₈	central extension (φ=1)	224		C4.76(C2^3xD7)	448,1368
C₄.₇₇(C₂³×D₇) = C₂×D₇×C₄○D₄	central extension (φ=1)	112		C4.77(C2^3xD7)	448,1375

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Extensions 1→N→G→Q→1 with N=C4 and Q=C23×D7

Extensions 1→N→G→Q→1 with N=C₄ and Q=C₂³×D₇