Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
470 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 470 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. #26033355 | C2 | semidirect |
| 2. #26021988 | C2 | semidirect |
| 3. #26020298 | C2 | semidirect |
| 4. #26018359 | C2 | semidirect |
| 16. #470×C89 | C4 | semidirect |
| 17. #469×C89 | C4 | semidirect |
| 24. #15667952 | D4 | semidirect |
| 144. C89 | #13077 | semidirect |
| 151. #470 | Dic89 | semidirect |
| 152. #469 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033355 | 2 |
| #26021988 | 2 |
| #26020298 | 2 |
| #26018359 | 2 |
| C89×#3060 | 2 |
| #13077 | 89 |