Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
558 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 558 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 |
|---|---|---|
| 2. #26020351 | C2 | semidirect |
| 4. #26018138 | C2 | semidirect |
| 16. #400×C89 | C4 | semidirect |
| 17. #399×C89 | C4 | semidirect |
| 18. #398×C89 | C4 | semidirect |
| 20. #397×C89 | C4 | semidirect |
| 189. C89 | #9012 | semidirect |
| 197. #400 | Dic89 | semidirect |
| 198. #399 | Dic89 | semidirect |
| 199. #398 | Dic89 | semidirect |
| 201. #397 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029293 | 2 |
| #26020351 | 2 |
| C4×#15667927 | 2 |
| #26018138 | 2 |
| C89×#2395 | 2 |
| #9012 | 89 |