Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
798 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 4. #26018785 | C2 | semidirect |
| 5. #26018582 | C2 | semidirect |
| 6. #26018105 | C2 | semidirect |
| 7. C89×#2583 | C2 | semidirect |
| 254. #2583 | D89 | semidirect |
| 260. C89 | #9943 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029510 | 2 |
| #26023587 | 2 |
| #26020197 | 2 |
| #26018785 | 2 |
| #26018582 | 2 |
| #26018105 | 2 |
| C89×#2583 | 2 |
| #9943 | 89 |