Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
384 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 384 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 |
|---|---|---|
| 2. C4×#15667945 | C2 | semidirect |
| 3. #26019013 | C2 | semidirect |
| 6. #26018109 | C2 | semidirect |
| 7. C89×#1285 | C2 | semidirect |
| 9. #19151725 | C4 | semidirect |
| 10. #19151722 | C4 | semidirect |
| 11. #19151675 | C4 | semidirect |
| 13. #19151663 | C4 | semidirect |
| 185. #1285 | D89 | semidirect |
| 186. C89 | #8697 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029221 | 2 |
| C4×#15667945 | 2 |
| #26019013 | 2 |
| #26018778 | 2 |
| #26018775 | 2 |
| #26018109 | 2 |
| C89×#1285 | 2 |
| #8697 | 89 |