Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
286 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 79 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. #26022064 | C2 | semidirect |
| 2. #26020401 | C2 | semidirect |
| 3. #26018246 | C2 | semidirect |
| 5. #26018240 | C2 | semidirect |
| 17. #499×C89 | C4 | semidirect |
| 18. #495×C89 | C4 | semidirect |
| 23. #442×C89 | C4 | semidirect |
| 24. #441×C89 | C4 | semidirect |
| 147. C89 | #11836 | semidirect |
| 149. #499 | Dic89 | semidirect |
| 150. #495 | Dic89 | semidirect |
| 155. #442 | Dic89 | semidirect |
| 156. #441 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022064 | 2 |
| #26020401 | 2 |
| #26018246 | 2 |
| #26018243 | 2 |
| #26018240 | 2 |
| #26018237 | 2 |
| C89×#3183 | 2 |
| #11836 | 89 |