# Extensions 1→N→G→Q→1 with N=Dic15 and Q=C23

Direct product G=N×Q with N=Dic15 and Q=C23
dρLabelID
C23×Dic15480C2^3xDic15480,1178

Semidirect products G=N:Q with N=Dic15 and Q=C23
extensionφ:Q→Out NdρLabelID
Dic151C23 = S3×D4×D5φ: C23/C2C22 ⊆ Out Dic15608+Dic15:1C2^3480,1097
Dic152C23 = C2×D5×C3⋊D4φ: C23/C2C22 ⊆ Out Dic15120Dic15:2C2^3480,1122
Dic153C23 = C2×S3×C5⋊D4φ: C23/C2C22 ⊆ Out Dic15120Dic15:3C2^3480,1123
Dic154C23 = C2×D4×D15φ: C23/C22C2 ⊆ Out Dic15120Dic15:4C2^3480,1169
Dic155C23 = C22×C157D4φ: C23/C22C2 ⊆ Out Dic15240Dic15:5C2^3480,1179
Dic156C23 = S3×C2×C4×D5φ: C23/C22C2 ⊆ Out Dic15120Dic15:6C2^3480,1086
Dic157C23 = C2×C20⋊D6φ: C23/C22C2 ⊆ Out Dic15120Dic15:7C2^3480,1089
Dic158C23 = C22×D5×Dic3φ: C23/C22C2 ⊆ Out Dic15240Dic15:8C2^3480,1112
Dic159C23 = C22×S3×Dic5φ: C23/C22C2 ⊆ Out Dic15240Dic15:9C2^3480,1115
Dic1510C23 = C22×C15⋊D4φ: C23/C22C2 ⊆ Out Dic15240Dic15:10C2^3480,1118
Dic1511C23 = C22×C4×D15φ: trivial image240Dic15:11C2^3480,1166

Non-split extensions G=N.Q with N=Dic15 and Q=C23
extensionφ:Q→Out NdρLabelID
Dic15.1C23 = C2×D5×Dic6φ: C23/C2C22 ⊆ Out Dic15240Dic15.1C2^3480,1073
Dic15.2C23 = C2×D205S3φ: C23/C2C22 ⊆ Out Dic15240Dic15.2C2^3480,1074
Dic15.3C23 = D20.38D6φ: C23/C2C22 ⊆ Out Dic152404Dic15.3C2^3480,1076
Dic15.4C23 = D20.39D6φ: C23/C2C22 ⊆ Out Dic152404-Dic15.4C2^3480,1077
Dic15.5C23 = C2×S3×Dic10φ: C23/C2C22 ⊆ Out Dic15240Dic15.5C2^3480,1078
Dic15.6C23 = C30.C24φ: C23/C2C22 ⊆ Out Dic152404Dic15.6C2^3480,1080
Dic15.7C23 = C2×D125D5φ: C23/C2C22 ⊆ Out Dic15240Dic15.7C2^3480,1084
Dic15.8C23 = D5×C4○D12φ: C23/C2C22 ⊆ Out Dic151204Dic15.8C2^3480,1090
Dic15.9C23 = S3×C4○D20φ: C23/C2C22 ⊆ Out Dic151204Dic15.9C2^3480,1091
Dic15.10C23 = D2025D6φ: C23/C2C22 ⊆ Out Dic151204Dic15.10C2^3480,1093
Dic15.11C23 = D2026D6φ: C23/C2C22 ⊆ Out Dic151204Dic15.11C2^3480,1094
Dic15.12C23 = C15⋊2- 1+4φ: C23/C2C22 ⊆ Out Dic152408-Dic15.12C2^3480,1096
Dic15.13C23 = D5×D42S3φ: C23/C2C22 ⊆ Out Dic151208-Dic15.13C2^3480,1098
Dic15.14C23 = S3×D42D5φ: C23/C2C22 ⊆ Out Dic151208-Dic15.14C2^3480,1099
Dic15.15C23 = D30.C23φ: C23/C2C22 ⊆ Out Dic151208+Dic15.15C2^3480,1100
Dic15.16C23 = D2013D6φ: C23/C2C22 ⊆ Out Dic151208-Dic15.16C2^3480,1101
Dic15.17C23 = D2014D6φ: C23/C2C22 ⊆ Out Dic151208+Dic15.17C2^3480,1102
Dic15.18C23 = D1214D10φ: C23/C2C22 ⊆ Out Dic151208+Dic15.18C2^3480,1103
Dic15.19C23 = D20.29D6φ: C23/C2C22 ⊆ Out Dic152408-Dic15.19C2^3480,1104
Dic15.20C23 = D12.29D10φ: C23/C2C22 ⊆ Out Dic152408-Dic15.20C2^3480,1106
Dic15.21C23 = S3×Q8×D5φ: C23/C2C22 ⊆ Out Dic151208-Dic15.21C2^3480,1107
Dic15.22C23 = D2016D6φ: C23/C2C22 ⊆ Out Dic151208-Dic15.22C2^3480,1110
Dic15.23C23 = C2×Dic5.D6φ: C23/C2C22 ⊆ Out Dic15240Dic15.23C2^3480,1113
Dic15.24C23 = C2×Dic3.D10φ: C23/C2C22 ⊆ Out Dic15240Dic15.24C2^3480,1116
Dic15.25C23 = C15⋊2+ 1+4φ: C23/C2C22 ⊆ Out Dic151204Dic15.25C2^3480,1125
Dic15.26C23 = C22×Dic30φ: C23/C22C2 ⊆ Out Dic15480Dic15.26C2^3480,1165
Dic15.27C23 = C2×D6011C2φ: C23/C22C2 ⊆ Out Dic15240Dic15.27C2^3480,1168
Dic15.28C23 = D46D30φ: C23/C22C2 ⊆ Out Dic151204Dic15.28C2^3480,1171
Dic15.29C23 = C2×Q8×D15φ: C23/C22C2 ⊆ Out Dic15240Dic15.29C2^3480,1172
Dic15.30C23 = Q8.15D30φ: C23/C22C2 ⊆ Out Dic152404Dic15.30C2^3480,1174
Dic15.31C23 = C4○D4×D15φ: C23/C22C2 ⊆ Out Dic151204Dic15.31C2^3480,1175
Dic15.32C23 = D48D30φ: C23/C22C2 ⊆ Out Dic151204+Dic15.32C2^3480,1176
Dic15.33C23 = D4.10D30φ: C23/C22C2 ⊆ Out Dic152404-Dic15.33C2^3480,1177
Dic15.34C23 = C2×D20⋊S3φ: C23/C22C2 ⊆ Out Dic15240Dic15.34C2^3480,1075
Dic15.35C23 = C2×D12⋊D5φ: C23/C22C2 ⊆ Out Dic15240Dic15.35C2^3480,1079
Dic15.36C23 = C2×D15⋊Q8φ: C23/C22C2 ⊆ Out Dic15240Dic15.36C2^3480,1082
Dic15.37C23 = C2×D6.D10φ: C23/C22C2 ⊆ Out Dic15240Dic15.37C2^3480,1083
Dic15.38C23 = D2024D6φ: C23/C22C2 ⊆ Out Dic151204Dic15.38C2^3480,1092
Dic15.39C23 = C30.33C24φ: C23/C22C2 ⊆ Out Dic152408+Dic15.39C2^3480,1105
Dic15.40C23 = D5×Q83S3φ: C23/C22C2 ⊆ Out Dic151208+Dic15.40C2^3480,1108
Dic15.41C23 = S3×Q82D5φ: C23/C22C2 ⊆ Out Dic151208+Dic15.41C2^3480,1109
Dic15.42C23 = D2017D6φ: C23/C22C2 ⊆ Out Dic151208+Dic15.42C2^3480,1111
Dic15.43C23 = C2×C30.C23φ: C23/C22C2 ⊆ Out Dic15240Dic15.43C2^3480,1114
Dic15.44C23 = C22×C15⋊Q8φ: C23/C22C2 ⊆ Out Dic15480Dic15.44C2^3480,1121
Dic15.45C23 = C2×D42D15φ: trivial image240Dic15.45C2^3480,1170
Dic15.46C23 = C2×Q83D15φ: trivial image240Dic15.46C2^3480,1173

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