Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1386 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 1386 conjugacy classes of subgroups — too many to draw. Only its 167 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 |
|---|---|---|
| 1. #26034016 | C2 | semidirect |
| 2. #26030343 | C2 | semidirect |
| 3. #26019271 | C2 | semidirect |
| 4. #26019169 | C2 | semidirect |
| 5. #26018759 | C2 | semidirect |
| 6. #26018593 | C2 | semidirect |
| 7. C89×#2397 | C2 | semidirect |
| 16. #19151916 | C22 | semidirect |
| 19. #19151732 | C22 | semidirect |
| 21. #19151655 | C22 | semidirect |
| 22. #19151331 | C22 | semidirect |
| 23. #19151322 | C22 | semidirect |
| 26. C2×C4×D4×C89 | C22 | semidirect |
| 28. #399×C89 | C22 | semidirect |
| 30. #392×C89 | C22 | semidirect |
| 31. #376×C89 | C22 | semidirect |
| 39. #15668012 | D4 | semidirect |
| 40. #15668009 | D4 | semidirect |
| 52. C4×D356 | D4 | semidirect |
| 221. #2397 | D89 | semidirect |
| 226. C89 | #18178 | semidirect |
| 237. C2×C4×D4 | C2×D89 | semidirect |
| 245. #399 | C2×D89 | semidirect |
| 247. #392 | C2×D89 | semidirect |
| 248. #376 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034016 | 2 |
| #26030343 | 2 |
| #26019271 | 2 |
| #26019169 | 2 |
| #26018759 | 2 |
| #26018593 | 2 |
| C89×#2397 | 2 |
| #18178 | 89 |