Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
772 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26029300 | C2 | semidirect |
| 3. #26020182 | C2 | semidirect |
| 4. #26020172 | C2 | semidirect |
| 5. #26018158 | C2 | semidirect |
| 6. #26018128 | C2 | semidirect |
| 7. C89×#1513 | C2 | semidirect |
| 11. #19151748 | C4 | semidirect |
| 13. #19151731 | C4 | semidirect |
| 279. #1513 | D89 | semidirect |
| 282. C89 | #9520 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029478 | 2 |
| #26029300 | 2 |
| #26020182 | 2 |
| #26020172 | 2 |
| #26018158 | 2 |
| #26018128 | 2 |
| C89×#1513 | 2 |
| #9520 | 89 |