Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
462 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 462 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. #26023058 | C2 | semidirect |
| 3. #26018854 | C2 | semidirect |
| 5. #26018118 | C2 | semidirect |
| 6. #26018107 | C2 | semidirect |
| 25. #501×C89 | C4 | semidirect |
| 26. #490×C89 | C4 | semidirect |
| 205. C89 | #9382 | semidirect |
| 208. #501 | Dic89 | semidirect |
| 209. #490 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023058 | 2 |
| #26021172 | 2 |
| #26018854 | 2 |
| #26018799 | 2 |
| #26018118 | 2 |
| #26018107 | 2 |
| C89×#3234 | 2 |
| #9382 | 89 |