Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
452 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 83 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. #26018282 | C2 | semidirect |
| 5. #26018280 | C2 | semidirect |
| 6. #26018278 | C2 | semidirect |
| 7. C89×#1354 | C2 | semidirect |
| 187. #1354 | D89 | semidirect |
| 190. C89 | #11721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023523 | 2 |
| #26019989 | 2 |
| #26018565 | 2 |
| #26018282 | 2 |
| #26018280 | 2 |
| #26018278 | 2 |
| C89×#1354 | 2 |
| #11721 | 89 |