Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
442 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 442 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 |
|---|---|---|
| 3. #26018276 | C2 | semidirect |
| 4. #26018252 | C2 | semidirect |
| 12. C2×#125×C89 | C4 | semidirect |
| 14. #399×C89 | C4 | semidirect |
| 17. #397×C89 | C4 | semidirect |
| 22. #383×C89 | C4 | semidirect |
| 182. C89 | #11732 | semidirect |
| 183. C2×#125 | Dic89 | semidirect |
| 187. #399 | Dic89 | semidirect |
| 190. #397 | Dic89 | semidirect |
| 195. #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 |
| #26018276 | 2 |
| #26018252 | 2 |
| C89×#2633 | 2 |
| #11732 | 89 |