Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
646 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 646 conjugacy classes of subgroups — too many to draw. Only its 135 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. #26033394 | C2 | semidirect |
| 2. #26032037 | C2 | semidirect |
| 3. #26022379 | C2 | semidirect |
| 4. #26022318 | C2 | semidirect |
| 5. #26022229 | C2 | semidirect |
| 6. #26022208 | C2 | semidirect |
| 7. #26022134 | C2 | semidirect |
| 8. #26022090 | C2 | semidirect |
| 9. C89×#2249 | C2 | semidirect |
| 12. #19152399 | C22 | semidirect |
| 13. #19152039 | C22 | semidirect |
| 20. #19152014 | C22 | semidirect |
| 21. #19151870 | C22 | semidirect |
| 27. #19151716 | C22 | semidirect |
| 28. #19151428 | C22 | semidirect |
| 29. #19151419 | C22 | semidirect |
| 30. #19151414 | C22 | semidirect |
| 31. #19151411 | C22 | semidirect |
| 32. #19151406 | C22 | semidirect |
| 33. #19151381 | C22 | semidirect |
| 34. C2×Q32×C89 | C22 | semidirect |
| 35. C2×SD32×C89 | C22 | semidirect |
| 37. #495×C89 | C22 | semidirect |
| 38. C4×C16×C89 | C22 | semidirect |
| 184. #2249 | D89 | semidirect |
| 191. C89 | #33857 | semidirect |
| 201. C2×Q32 | C2×D89 | semidirect |
| 203. C2×SD32 | C2×D89 | semidirect |
| 206. #495 | C2×D89 | semidirect |
| 220. C4×C16 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033394 | 2 |
| #26032037 | 2 |
| #26022379 | 2 |
| #26022318 | 2 |
| #26022229 | 2 |
| #26022208 | 2 |
| #26022134 | 2 |
| #26022090 | 2 |
| C89×#2249 | 2 |
| #33857 | 89 |