Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
960 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 960 conjugacy classes of subgroups — too many to draw. Only its 155 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. C2×#19152346 | C2 | semidirect |
| 2. #26031235 | C2 | semidirect |
| 3. #26019573 | C2 | semidirect |
| 4. #26019544 | C2 | semidirect |
| 5. #26018879 | C2 | semidirect |
| 6. #26018849 | C2 | semidirect |
| 7. C89×#3142 | C2 | semidirect |
| 15. #19151985 | C22 | semidirect |
| 16. #19151960 | C22 | semidirect |
| 21. #19151340 | C22 | semidirect |
| 22. #19151337 | C22 | semidirect |
| 25. #491×C89 | C22 | semidirect |
| 26. #490×C89 | C22 | semidirect |
| 167. #3142 | D89 | semidirect |
| 172. C89 | #19001 | semidirect |
| 183. #491 | C2×D89 | semidirect |
| 184. #490 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152346 | 2 |
| #26031235 | 2 |
| #26019573 | 2 |
| #26019544 | 2 |
| #26018879 | 2 |
| #26018849 | 2 |
| C89×#3142 | 2 |
| #19001 | 89 |