Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
456 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26023358 | C2 | semidirect |
| 2. #26018879 | C2 | semidirect |
| 4. #26018146 | C2 | semidirect |
| 16. #491×C89 | C4 | semidirect |
| 17. #490×C89 | C4 | semidirect |
| 123. C89 | #9442 | semidirect |
| 126. #491 | Dic89 | semidirect |
| 127. #490 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023358 | 2 |
| #26018879 | 2 |
| #26018760 | 2 |
| #26018146 | 2 |
| C89×#3142 | 2 |
| #9442 | 89 |