Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
528 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 131 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. #26033261 | C2 | semidirect |
| 2. #26022517 | C2 | semidirect |
| 3. #26022316 | C2 | semidirect |
| 4. #26022304 | C2 | semidirect |
| 5. #26022285 | C2 | semidirect |
| 6. #26022160 | C2 | semidirect |
| 7. #26022117 | C2 | semidirect |
| 8. C4×D1424 | C2 | semidirect |
| 9. C89×#2249 | C2 | semidirect |
| 152. #2249 | D89 | semidirect |
| 159. C89 | #33970 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033261 | 2 |
| #26022517 | 2 |
| #26022316 | 2 |
| #26022304 | 2 |
| #26022285 | 2 |
| #26022160 | 2 |
| #26022117 | 2 |
| C4×D1424 | 2 |
| C89×#2249 | 2 |
| #33970 | 89 |