Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
958 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 958 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26022605 | C2 | semidirect |
| 2. #26020196 | C2 | semidirect |
| 3. #26018579 | C2 | semidirect |
| 4. #26018104 | C2 | semidirect |
| 16. #393×C89 | C4 | semidirect |
| 17. #392×C89 | C4 | semidirect |
| 27. C2×C4×Dic89 | D4 | semidirect |
| 37. C22×Q8×C89 | C2×C4 | semidirect |
| 40. C22×D4×C89 | C2×C4 | semidirect |
| 54. #95×C89 | C2×C4 | semidirect |
| 127. C23×C89 | #104 | semidirect |
| 204. C89 | #9475 | semidirect |
| 211. #393 | Dic89 | semidirect |
| 212. #392 | Dic89 | semidirect |
| 224. C22×Q8 | C2×Dic89 | semidirect |
| 227. C22×D4 | C2×Dic89 | semidirect |
| 253. #95 | C2×Dic89 | semidirect |
| 326. C23 | #15667939 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022605 | 2 |
| #26020196 | 2 |
| #26018579 | 2 |
| #26018104 | 2 |
| C89×#2404 | 2 |
| #9475 | 89 |