Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
606 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 606 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. #26018570 | 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 |
| 211. C89 | #11726 | semidirect |
| 214. C2×C4×D4 | Dic89 | semidirect |
| 219. #399 | Dic89 | semidirect |
| 222. #392 | Dic89 | semidirect |
| 225. #376 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15667927 | 2 |
| #26018570 | 2 |
| #26018276 | 2 |
| #26018249 | 2 |
| C89×#2397 | 2 |
| #11726 | 89 |