Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
424 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 63 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. #26022186 | C2 | semidirect |
| 4. #26018265 | C2 | semidirect |
| 5. #26018264 | C2 | semidirect |
| 7. C89×#2188 | C2 | semidirect |
| 122. C22×D89 | Q32 | semidirect |
| 185. #2188 | D89 | semidirect |
| 190. C89 | #12106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031023 | 2 |
| #26022186 | 2 |
| #26021259 | 2 |
| #26018265 | 2 |
| #26018264 | 2 |
| #26018175 | 2 |
| C89×#2188 | 2 |
| #12106 | 89 |