Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
372 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 63 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. #26022396 | C2 | semidirect |
| 3. #26019762 | C2 | semidirect |
| 4. #26018295 | C2 | semidirect |
| 5. #26018220 | C2 | semidirect |
| 6. #26018211 | C2 | semidirect |
| 7. C89×#2243 | C2 | semidirect |
| 18. C4⋊#13083549 | C22 | semidirect |
| 20. #19151349 | C22 | semidirect |
| 22. #500×C89 | C22 | semidirect |
| 26. #346×C89 | C22 | semidirect |
| 78. D712 | SD16 | semidirect |
| 168. #2243 | D89 | semidirect |
| 174. C89 | #12378 | semidirect |
| 177. #500 | C2×D89 | semidirect |
| 191. #346 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031861 | 2 |
| #26022396 | 2 |
| #26019762 | 2 |
| #26018295 | 2 |
| #26018220 | 2 |
| #26018211 | 2 |
| C89×#2243 | 2 |
| #12378 | 89 |