Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
564 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26030988 | C2 | semidirect |
| 2. #26029157 | C2 | semidirect |
| 3. #26022465 | C2 | semidirect |
| 4. #26022424 | C2 | semidirect |
| 5. #26022423 | C2 | semidirect |
| 6. #26022325 | C2 | semidirect |
| 7. #26022196 | C2 | semidirect |
| 8. #26022153 | C2 | semidirect |
| 9. #26022151 | C2 | semidirect |
| 10. #26022063 | C2 | semidirect |
| 11. C89×#2213 | C2 | semidirect |
| 16. #19151996 | C22 | semidirect |
| 26. #19151710 | C22 | semidirect |
| 30. #19151422 | C22 | semidirect |
| 31. #19151421 | C22 | semidirect |
| 32. #19151419 | C22 | semidirect |
| 33. #19151411 | C22 | semidirect |
| 37. #19151375 | C22 | semidirect |
| 39. #493×C89 | C22 | semidirect |
| 41. #364×C89 | C22 | semidirect |
| 42. #361×C89 | C22 | semidirect |
| 109. Dic356 | #41 | semidirect |
| 114. D712 | #41 | semidirect |
| 142. Q16×C89 | #41 | semidirect |
| 148. D8×C89 | #41 | semidirect |
| 227. #2213 | D89 | semidirect |
| 232. C89 | #33688 | semidirect |
| 239. #493 | C2×D89 | semidirect |
| 257. #364 | C2×D89 | semidirect |
| 259. #361 | C2×D89 | semidirect |
| 336. Q16 | #13083573 | semidirect |
| 347. D8 | #13083573 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030988 | 2 |
| #26029157 | 2 |
| #26022465 | 2 |
| #26022424 | 2 |
| #26022423 | 2 |
| #26022325 | 2 |
| #26022196 | 2 |
| #26022153 | 2 |
| #26022151 | 2 |
| #26022063 | 2 |
| C89×#2213 | 2 |
| #33688 | 89 |