Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
820 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 131 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. #26021085 | C2 | semidirect |
| 2. #26018974 | C2 | semidirect |
| 3. #26018887 | C2 | semidirect |
| 4. #26018760 | C2 | semidirect |
| 6. #19151655 | C22 | semidirect |
| 7. #19151622 | C22 | semidirect |
| 9. #19151444 | C22 | semidirect |
| 16. #555×C89 | C4 | semidirect |
| 18. D42×C89 | C4 | semidirect |
| 160. C89 | #8491 | semidirect |
| 163. #555 | Dic89 | semidirect |
| 165. D42 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021085 | 2 |
| #26018974 | 2 |
| #26018887 | 2 |
| #26018760 | 2 |
| C89×#3549 | 2 |
| #8491 | 89 |