Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1250 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 1250 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 |
|---|---|---|
| 2. #26030374 | C2 | semidirect |
| 3. #26019237 | C2 | semidirect |
| 4. #26019203 | C2 | semidirect |
| 5. #26018759 | C2 | semidirect |
| 6. #26018593 | C2 | semidirect |
| 7. C89×#2398 | C2 | semidirect |
| 16. #19151911 | C22 | semidirect |
| 19. #19151737 | C22 | semidirect |
| 21. #19151655 | C22 | semidirect |
| 22. #19151331 | C22 | semidirect |
| 23. #19151322 | C22 | semidirect |
| 24. C2×C4×Q8×C89 | C22 | semidirect |
| 27. #397×C89 | C22 | semidirect |
| 29. #393×C89 | C22 | semidirect |
| 31. #376×C89 | C22 | semidirect |
| 205. #2398 | D89 | semidirect |
| 210. C89 | #18179 | semidirect |
| 219. C2×C4×Q8 | C2×D89 | semidirect |
| 228. #397 | C2×D89 | semidirect |
| 230. #393 | C2×D89 | semidirect |
| 232. #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 |
| #26030374 | 2 |
| #26019237 | 2 |
| #26019203 | 2 |
| #26018759 | 2 |
| #26018593 | 2 |
| C89×#2398 | 2 |
| #18179 | 89 |