Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
552 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 552 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 |
|---|---|---|
| 2. #26022852 | C2 | semidirect |
| 5. #26018581 | C2 | semidirect |
| 6. #26018138 | C2 | semidirect |
| 7. C89×#1297 | C2 | semidirect |
| 11. #19151538 | C4 | semidirect |
| 12. #19151516 | C4 | semidirect |
| 199. #1297 | D89 | semidirect |
| 200. C89 | #9414 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025727 | 2 |
| #26022852 | 2 |
| #26018769 | 2 |
| #26018767 | 2 |
| #26018581 | 2 |
| #26018138 | 2 |
| C89×#1297 | 2 |
| #9414 | 89 |