Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
512 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 93 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. #19151504 | C4 | semidirect |
| 15. #19151464 | C4 | semidirect |
| 188. C89 | #9460 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26024737 | 2 |
| #26022853 | 2 |
| #26020330 | 2 |
| #26018786 | 2 |
| #26018784 | 2 |
| #26018105 | 2 |
| C89×#1284 | 2 |
| #9460 | 89 |