Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1230 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 1230 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. #26031054 | C2 | semidirect |
| 3. #26019254 | C2 | semidirect |
| 4. #26019220 | C2 | semidirect |
| 5. #26018767 | C2 | semidirect |
| 6. #26018582 | C2 | semidirect |
| 7. C89×#2583 | C2 | semidirect |
| 17. #19151911 | C22 | semidirect |
| 20. #19151737 | C22 | semidirect |
| 22. #19151331 | C22 | semidirect |
| 23. #19151324 | C22 | semidirect |
| 26. #398×C89 | C22 | semidirect |
| 27. #395×C89 | C22 | semidirect |
| 216. #2583 | D89 | semidirect |
| 221. C89 | #18325 | semidirect |
| 238. #398 | C2×D89 | semidirect |
| 239. #395 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152179 | 2 |
| #26031054 | 2 |
| #26019254 | 2 |
| #26019220 | 2 |
| #26018767 | 2 |
| #26018582 | 2 |
| C89×#2583 | 2 |
| #18325 | 89 |