Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
610 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 12. #19151538 | C4 | semidirect |
| 13. #19151530 | C4 | semidirect |
| 191. C89 | #9478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26024541 | 2 |
| #26022607 | 2 |
| #26020352 | 2 |
| #26020349 | 2 |
| #26018581 | 2 |
| #26018104 | 2 |
| C89×#1284 | 2 |
| #9478 | 89 |