Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
280 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 79 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. #26022525 | C2 | semidirect |
| 4. #26019846 | C2 | semidirect |
| 6. #26018168 | C2 | semidirect |
| 7. C89×#2241 | C2 | semidirect |
| 56. #13083549 | SD16 | semidirect |
| 106. #2241 | D89 | semidirect |
| 111. C89 | #12508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022525 | 2 |
| #26022509 | 2 |
| #26022476 | 2 |
| #26019846 | 2 |
| #26019845 | 2 |
| #26018168 | 2 |
| C89×#2241 | 2 |
| #12508 | 89 |