Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
784 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 111 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. #26029281 | C2 | semidirect |
| 2. #26020196 | C2 | semidirect |
| 3. C4×#15667927 | C2 | semidirect |
| 4. #26018138 | C2 | semidirect |
| 17. #395×C89 | C4 | semidirect |
| 19. #394×C89 | C4 | semidirect |
| 20. #393×C89 | C4 | semidirect |
| 22. #392×C89 | C4 | semidirect |
| 25. C2×#13083558 | D4 | semidirect |
| 138. C23×C89 | #104 | semidirect |
| 225. C89 | #9009 | semidirect |
| 235. #395 | Dic89 | semidirect |
| 237. #394 | Dic89 | semidirect |
| 238. #393 | Dic89 | semidirect |
| 240. #392 | Dic89 | semidirect |
| 358. C23 | #15667939 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029281 | 2 |
| #26020196 | 2 |
| C4×#15667927 | 2 |
| #26018138 | 2 |
| C89×#2388 | 2 |
| #9009 | 89 |