Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
366 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 61 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. #26032057 | C2 | semidirect |
| 2. #26022329 | C2 | semidirect |
| 3. #26022328 | C2 | semidirect |
| 4. #26019858 | C2 | semidirect |
| 5. #26018290 | C2 | semidirect |
| 6. #26018226 | C2 | semidirect |
| 7. C89×#1335 | C2 | semidirect |
| 150. #1335 | D89 | semidirect |
| 151. C89 | #12311 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26032057 | 2 |
| #26022329 | 2 |
| #26022328 | 2 |
| #26019858 | 2 |
| #26018290 | 2 |
| #26018226 | 2 |
| C89×#1335 | 2 |
| #12311 | 89 |