Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
416 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26029349 | C2 | semidirect |
| 3. #26018765 | C2 | semidirect |
| 6. #26018080 | C2 | semidirect |
| 7. C89×#1287 | C2 | semidirect |
| 10. #19151978 | C4 | semidirect |
| 11. #19151971 | C4 | semidirect |
| 12. #19151949 | C4 | semidirect |
| 13. #19151945 | C4 | semidirect |
| 173. #1287 | D89 | semidirect |
| 175. C89 | #9282 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031210 | 2 |
| #26029349 | 2 |
| #26018765 | 2 |
| #26018761 | 2 |
| #26018720 | 2 |
| #26018080 | 2 |
| C89×#1287 | 2 |
| #9282 | 89 |