Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
628 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 87 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. #26018371 | C2 | semidirect |
| 5. #26018370 | C2 | semidirect |
| 6. #26018369 | C2 | semidirect |
| 7. C89×#1390 | C2 | semidirect |
| 9. C2×#15667968 | C4 | semidirect |
| 10. C22×#13083553 | C4 | semidirect |
| 19. #19151477 | C4 | semidirect |
| 20. #19151475 | C4 | semidirect |
| 266. #1390 | D89 | semidirect |
| 267. C89 | #12855 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022839 | 2 |
| #26020177 | 2 |
| #26020168 | 2 |
| #26018371 | 2 |
| #26018370 | 2 |
| #26018369 | 2 |
| C89×#1390 | 2 |
| #12855 | 89 |