Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
786 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 786 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. #26018593 | C2 | semidirect |
| 3. #26018249 | C2 | semidirect |
| 8. #19151365 | C22 | semidirect |
| 10. #19151322 | C22 | semidirect |
| 11. C23×D4×C89 | C4 | semidirect |
| 15. #394×C89 | C4 | semidirect |
| 18. #380×C89 | C4 | semidirect |
| 197. C89 | #11772 | semidirect |
| 198. C23×D4 | Dic89 | semidirect |
| 204. #394 | Dic89 | semidirect |
| 207. #380 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15667927 | 2 |
| #26018593 | 2 |
| #26018249 | 2 |
| C89×#2408 | 2 |
| #11772 | 89 |