Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
582 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 91 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. #26020240 | C2 | semidirect |
| 2. #26018590 | C2 | semidirect |
| 3. #26018276 | C2 | semidirect |
| 4. #26018249 | C2 | semidirect |
| 14. C2×C4×D4×C89 | C4 | semidirect |
| 17. #399×C89 | C4 | semidirect |
| 20. #392×C89 | C4 | semidirect |
| 22. #376×C89 | C4 | semidirect |
| 219. C89 | #11821 | semidirect |
| 222. C2×C4×D4 | Dic89 | semidirect |
| 227. #399 | Dic89 | semidirect |
| 230. #392 | Dic89 | semidirect |
| 233. #376 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020240 | 2 |
| #26018590 | 2 |
| #26018276 | 2 |
| #26018249 | 2 |
| C89×#2397 | 2 |
| #11821 | 89 |