Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
552 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 552 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. #26022855 | C2 | semidirect |
| 3. #26018582 | C2 | semidirect |
| 4. #26018138 | C2 | semidirect |
| 15. #400×C89 | C4 | semidirect |
| 16. #394×C89 | C4 | semidirect |
| 158. C89 | #9414 | semidirect |
| 162. #400 | Dic89 | semidirect |
| 163. #394 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022855 | 2 |
| #26018768 | 2 |
| #26018582 | 2 |
| #26018138 | 2 |
| C89×#2591 | 2 |
| #9414 | 89 |