Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
648 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 95 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. C4×#15667927 | C2 | semidirect |
| 2. #26018573 | C2 | semidirect |
| 3. #26018273 | C2 | semidirect |
| 4. #26018249 | C2 | semidirect |
| 12. C22×#41×C89 | C4 | semidirect |
| 15. #395×C89 | C4 | semidirect |
| 17. #394×C89 | C4 | semidirect |
| 22. C4×C22⋊C4×C89 | C4 | semidirect |
| 216. C89 | #11725 | semidirect |
| 217. C22×#41 | Dic89 | semidirect |
| 222. #395 | Dic89 | semidirect |
| 224. #394 | Dic89 | semidirect |
| 230. C4×C22⋊C4 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15667927 | 2 |
| #26018573 | 2 |
| #26018273 | 2 |
| #26018249 | 2 |
| C89×#2388 | 2 |
| #11725 | 89 |