Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1314 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 1314 conjugacy classes of subgroups — too many to draw. Only its 187 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #26030183 | C2 | semidirect |
| 3. #26021469 | C2 | semidirect |
| 4. #26020695 | C2 | semidirect |
| 5. #26020461 | C2 | semidirect |
| 6. #26020205 | C2 | semidirect |
| 7. #26020180 | C2 | semidirect |
| 8. C89×#2297 | C2 | semidirect |
| 19. #19151638 | C22 | semidirect |
| 22. C2×#15667931 | C22 | semidirect |
| 24. #19151562 | C22 | semidirect |
| 25. #19151358 | C22 | semidirect |
| 27. C2×#117×C89 | C22 | semidirect |
| 28. C22×C42×C89 | C22 | semidirect |
| 29. #391×C89 | C22 | semidirect |
| 218. #2297 | D89 | semidirect |
| 224. C89 | #24021 | semidirect |
| 234. C2×#117 | C2×D89 | semidirect |
| 235. C22×C42 | C2×D89 | semidirect |
| 244. #391 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033896 | 2 |
| #26030183 | 2 |
| #26021469 | 2 |
| #26020695 | 2 |
| #26020461 | 2 |
| #26020205 | 2 |
| #26020180 | 2 |
| C89×#2297 | 2 |
| #24021 | 89 |