Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
500 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 91 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. C4×#15667927 | C2 | semidirect |
| 2. #26018570 | C2 | semidirect |
| 3. #26018273 | C2 | semidirect |
| 4. #26018249 | C2 | semidirect |
| 12. C2×#124×C89 | C4 | semidirect |
| 15. #393×C89 | C4 | semidirect |
| 18. #392×C89 | C4 | semidirect |
| 22. #383×C89 | C4 | semidirect |
| 203. C89 | #11730 | semidirect |
| 204. C2×#124 | Dic89 | semidirect |
| 209. #393 | Dic89 | semidirect |
| 212. #392 | Dic89 | semidirect |
| 216. #383 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15667927 | 2 |
| #26018570 | 2 |
| #26018273 | 2 |
| #26018249 | 2 |
| C89×#2631 | 2 |
| #11730 | 89 |