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. #26030991 | C2 | semidirect |
| 2. #26029157 | C2 | semidirect |
| 3. #26022468 | C2 | semidirect |
| 4. #26022420 | C2 | semidirect |
| 5. #26022329 | C2 | semidirect |
| 6. #26022328 | C2 | semidirect |
| 7. #26022199 | C2 | semidirect |
| 8. #26022149 | C2 | semidirect |
| 9. #26022147 | C2 | semidirect |
| 10. #26022063 | C2 | semidirect |
| 11. C89×#2230 | C2 | semidirect |
| 17. #19151975 | C22 | semidirect |
| 27. #19151709 | C22 | semidirect |
| 31. #19151420 | C22 | semidirect |
| 32. #19151419 | C22 | semidirect |
| 33. #19151412 | C22 | semidirect |
| 34. #19151410 | C22 | semidirect |
| 37. #19151375 | C22 | semidirect |
| 38. #498×C89 | C22 | semidirect |
| 40. #365×C89 | C22 | semidirect |
| 41. #364×C89 | C22 | semidirect |
| 111. Dic356 | #41 | semidirect |
| 120. D712 | #41 | semidirect |
| 144. Q16×C89 | #41 | semidirect |
| 146. D8×C89 | #41 | semidirect |
| 225. #2230 | D89 | semidirect |
| 232. C89 | #33688 | semidirect |
| 238. #498 | C2×D89 | semidirect |
| 255. #365 | C2×D89 | semidirect |
| 257. #364 | C2×D89 | semidirect |
| 336. Q16 | #13083575 | semidirect |
| 347. D8 | #13083575 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030991 | 2 |
| #26029157 | 2 |
| #26022468 | 2 |
| #26022420 | 2 |
| #26022329 | 2 |
| #26022328 | 2 |
| #26022199 | 2 |
| #26022149 | 2 |
| #26022147 | 2 |
| #26022063 | 2 |
| C89×#2230 | 2 |
| #33688 | 89 |