Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
542 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26023137 | C2 | semidirect |
| 3. #26020351 | C2 | semidirect |
| 5. #26018157 | C2 | semidirect |
| 6. #26018137 | C2 | semidirect |
| 26. #428×C89 | C4 | semidirect |
| 27. #418×C89 | C4 | semidirect |
| 210. C89 | #9367 | semidirect |
| 216. #428 | Dic89 | semidirect |
| 217. #418 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023137 | 2 |
| #26021089 | 2 |
| #26020351 | 2 |
| #26018768 | 2 |
| #26018157 | 2 |
| #26018137 | 2 |
| C89×#3094 | 2 |
| #9367 | 89 |