# Extensions 1→N→G→Q→1 with N=D56 and Q=C22

Direct product G=N×Q with N=D56 and Q=C22
dρLabelID
C22×D56224C2^2xD56448,1193

Semidirect products G=N:Q with N=D56 and Q=C22
extensionφ:Q→Out NdρLabelID
D561C22 = D7×C8⋊C22φ: C22/C1C22 ⊆ Out D56568+D56:1C2^2448,1225
D562C22 = D85D14φ: C22/C1C22 ⊆ Out D561128+D56:2C2^2448,1227
D563C22 = D56⋊C22φ: C22/C1C22 ⊆ Out D561128+D56:3C2^2448,1230
D564C22 = C56.C23φ: C22/C1C22 ⊆ Out D561128+D56:4C2^2448,1231
D565C22 = D7×D16φ: C22/C1C22 ⊆ Out D561124+D56:5C2^2448,444
D566C22 = D112⋊C2φ: C22/C1C22 ⊆ Out D561124+D56:6C2^2448,448
D567C22 = C2×D112φ: C22/C2C2 ⊆ Out D56224D56:7C2^2448,436
D568C22 = C16⋊D14φ: C22/C2C2 ⊆ Out D561124+D56:8C2^2448,442
D569C22 = C2×C8⋊D14φ: C22/C2C2 ⊆ Out D56112D56:9C2^2448,1199
D5610C22 = C56.9C23φ: C22/C2C2 ⊆ Out D561124D56:10C2^2448,1201
D5611C22 = D4.11D28φ: C22/C2C2 ⊆ Out D561124D56:11C2^2448,1204
D5612C22 = D4.12D28φ: C22/C2C2 ⊆ Out D561124+D56:12C2^2448,1205
D5613C22 = C2×C7⋊D16φ: C22/C2C2 ⊆ Out D56224D56:13C2^2448,680
D5614C22 = D8.D14φ: C22/C2C2 ⊆ Out D561124D56:14C2^2448,681
D5615C22 = C2×D7×D8φ: C22/C2C2 ⊆ Out D56112D56:15C2^2448,1207
D5616C22 = D813D14φ: C22/C2C2 ⊆ Out D561124D56:16C2^2448,1210
D5617C22 = C2×Q8.D14φ: C22/C2C2 ⊆ Out D56224D56:17C2^2448,1218
D5618C22 = D7×C4○D8φ: C22/C2C2 ⊆ Out D561124D56:18C2^2448,1220
D5619C22 = D815D14φ: C22/C2C2 ⊆ Out D561124+D56:19C2^2448,1222
D5620C22 = C2×D56⋊C2φ: C22/C2C2 ⊆ Out D56112D56:20C2^2448,1212
D5621C22 = D28.29D4φ: C22/C2C2 ⊆ Out D561124D56:21C2^2448,1215
D5622C22 = D810D14φ: C22/C2C2 ⊆ Out D561124D56:22C2^2448,1221
D5623C22 = C2×D567C2φ: trivial image224D56:23C2^2448,1194

Non-split extensions G=N.Q with N=D56 and Q=C22
extensionφ:Q→Out NdρLabelID
D56.1C22 = D8⋊D14φ: C22/C1C22 ⊆ Out D561124D56.1C2^2448,445
D56.2C22 = D7×SD32φ: C22/C1C22 ⊆ Out D561124D56.2C2^2448,447
D56.3C22 = SD323D7φ: C22/C1C22 ⊆ Out D562244D56.3C2^2448,450
D56.4C22 = Q32⋊D7φ: C22/C1C22 ⊆ Out D562244D56.4C2^2448,452
D56.5C22 = Q323D7φ: C22/C1C22 ⊆ Out D562244+D56.5C2^2448,453
D56.6C22 = C2×C112⋊C2φ: C22/C2C2 ⊆ Out D56224D56.6C2^2448,437
D56.7C22 = D1127C2φ: C22/C2C2 ⊆ Out D562242D56.7C2^2448,438
D56.8C22 = C16.D14φ: C22/C2C2 ⊆ Out D562244-D56.8C2^2448,443
D56.9C22 = C2×C7⋊SD32φ: C22/C2C2 ⊆ Out D56224D56.9C2^2448,712
D56.10C22 = Q16.D14φ: C22/C2C2 ⊆ Out D562244D56.10C2^2448,713
D56.11C22 = Q16⋊D14φ: C22/C2C2 ⊆ Out D561124+D56.11C2^2448,727
D56.12C22 = C56.30C23φ: C22/C2C2 ⊆ Out D562244D56.12C2^2448,728
D56.13C22 = D28.30D4φ: C22/C2C2 ⊆ Out D562244D56.13C2^2448,1219
D56.14C22 = D4.13D28φ: trivial image2244-D56.14C2^2448,1206

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