Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
778 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 778 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. C2×#19151365 | C2 | semidirect |
| 2. #26018579 | C2 | semidirect |
| 3. #26018273 | C2 | semidirect |
| 4. #26018249 | C2 | semidirect |
| 12. C22×#41×C89 | C4 | semidirect |
| 15. #393×C89 | C4 | semidirect |
| 17. #392×C89 | C4 | semidirect |
| 22. #381×C89 | C4 | semidirect |
| 35. C22×Q8×C89 | C2×C4 | semidirect |
| 39. C22×D4×C89 | C2×C4 | semidirect |
| 58. #95×C89 | C2×C4 | semidirect |
| 59. #95×C89 | C2×C4 | semidirect |
| 257. C89 | #11753 | semidirect |
| 258. C22×#41 | Dic89 | semidirect |
| 263. #393 | Dic89 | semidirect |
| 265. #392 | Dic89 | semidirect |
| 270. #381 | Dic89 | semidirect |
| 279. C22×Q8 | C2×Dic89 | semidirect |
| 283. C22×D4 | C2×Dic89 | semidirect |
| 310. #95 | C2×Dic89 | semidirect |
| 311. #95 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151365 | 2 |
| #26018579 | 2 |
| #26018273 | 2 |
| #26018249 | 2 |
| C89×#2404 | 2 |
| #11753 | 89 |