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. #26022188 | C2 | semidirect |
| 3. #26022185 | C2 | semidirect |
| 5. #26018263 | C2 | semidirect |
| 7. C89×#1348 | C2 | semidirect |
| 122. C22×D89 | Q32 | semidirect |
| 188. #1348 | 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 |
| #26022188 | 2 |
| #26022185 | 2 |
| #26021263 | 2 |
| #26018263 | 2 |
| #26018175 | 2 |
| C89×#1348 | 2 |
| #12106 | 89 |