Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
530 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 4. #26018772 | C2 | semidirect |
| 5. #26018106 | C2 | semidirect |
| 6. #26018105 | C2 | semidirect |
| 7. C89×#1508 | C2 | semidirect |
| 15. #19151529 | C4 | semidirect |
| 17. #19151524 | C4 | semidirect |
| 18. #19151517 | C4 | semidirect |
| 20. #19151509 | C4 | semidirect |
| 236. #1508 | D89 | semidirect |
| 239. C89 | #9184 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029291 | 2 |
| #26026170 | 2 |
| C4×#15667926 | 2 |
| #26018772 | 2 |
| #26018106 | 2 |
| #26018105 | 2 |
| C89×#1508 | 2 |
| #9184 | 89 |