Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
770 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26021099 | C2 | semidirect |
| 3. #26018860 | C2 | semidirect |
| 4. #26018715 | C2 | semidirect |
| 5. #26018669 | C2 | semidirect |
| 6. #26018605 | C2 | semidirect |
| 7. C89×#1557 | C2 | semidirect |
| 22. #19151651 | C22 | semidirect |
| 25. C4×#13083558 | C22 | semidirect |
| 33. #432×C89 | C22 | semidirect |
| 34. #423×C89 | C22 | semidirect |
| 279. #1557 | D89 | semidirect |
| 284. C89 | #8483 | semidirect |
| 300. #432 | C2×D89 | semidirect |
| 302. #423 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034775 | 2 |
| #26021099 | 2 |
| #26018860 | 2 |
| #26018715 | 2 |
| #26018669 | 2 |
| #26018605 | 2 |
| C89×#1557 | 2 |
| #8483 | 89 |