Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
488 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 488 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 |
|---|---|---|
| 9. C22×#13083553 | C4 | semidirect |
| 17. #19151473 | C4 | semidirect |
| 18. #19151471 | C4 | semidirect |
| 20. #19151456 | C4 | semidirect |
| 231. C89 | #13297 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025598 | 2 |
| #26020242 | 2 |
| #99×Dic89 | 2 |
| #26018371 | 2 |
| #26018370 | 2 |
| #26018369 | 2 |
| C89×#1390 | 2 |
| #13297 | 89 |