Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
476 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 81 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. #26031442 | C2 | semidirect |
| 3. #26018721 | C2 | semidirect |
| 4. #26018670 | C2 | semidirect |
| 5. #26018608 | C2 | semidirect |
| 6. #26018124 | C2 | semidirect |
| 7. C89×#3142 | C2 | semidirect |
| 192. #3142 | D89 | semidirect |
| 197. C89 | #10122 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031442 | 2 |
| #26031243 | 2 |
| #26018721 | 2 |
| #26018670 | 2 |
| #26018608 | 2 |
| #26018124 | 2 |
| C89×#3142 | 2 |
| #10122 | 89 |