Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
532 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 532 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. C4×#15667927 | C2 | semidirect |
| 2. #26018593 | C2 | semidirect |
| 3. #26018252 | C2 | semidirect |
| 4. #26018249 | C2 | semidirect |
| 13. C2×#121×C89 | C4 | semidirect |
| 15. #398×C89 | C4 | semidirect |
| 17. #394×C89 | C4 | semidirect |
| 22. C2×#95×C89 | C4 | semidirect |
| 205. C89 | #11775 | semidirect |
| 207. C2×#121 | Dic89 | semidirect |
| 211. #398 | Dic89 | semidirect |
| 213. #394 | Dic89 | semidirect |
| 219. C2×#95 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15667927 | 2 |
| #26018593 | 2 |
| #26018252 | 2 |
| #26018249 | 2 |
| C89×#2543 | 2 |
| #11775 | 89 |