Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1078 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 1078 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. #26034657 | C2 | semidirect |
| 2. #26031243 | C2 | semidirect |
| 3. #26019556 | C2 | semidirect |
| 4. #26019540 | C2 | semidirect |
| 5. #26018887 | C2 | semidirect |
| 6. #26018862 | C2 | semidirect |
| 7. C89×#3150 | C2 | semidirect |
| 16. #19151985 | C22 | semidirect |
| 17. #19151960 | C22 | semidirect |
| 21. #19151655 | C22 | semidirect |
| 22. #19151338 | C22 | semidirect |
| 23. #19151337 | C22 | semidirect |
| 26. #532×C89 | C22 | semidirect |
| 28. #497×C89 | C22 | semidirect |
| 30. #496×C89 | C22 | semidirect |
| 31. C2×#97×C89 | C22 | semidirect |
| 193. #3150 | D89 | semidirect |
| 198. C89 | #19052 | semidirect |
| 209. #532 | C2×D89 | semidirect |
| 211. #497 | C2×D89 | semidirect |
| 214. #496 | C2×D89 | semidirect |
| 220. C2×#97 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034657 | 2 |
| #26031243 | 2 |
| #26019556 | 2 |
| #26019540 | 2 |
| #26018887 | 2 |
| #26018862 | 2 |
| C89×#3150 | 2 |
| #19052 | 89 |