Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1328 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1328 conjugacy classes of subgroups — too many to draw. Only its 291 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 |
|---|---|---|
| 1. #26034964 | C2 | semidirect |
| 2. #26028947 | C2 | semidirect |
| 3. #26020671 | C2 | semidirect |
| 4. #26020540 | C2 | semidirect |
| 5. #26020203 | C2 | semidirect |
| 6. #26020054 | C2 | semidirect |
| 12. C23×#10623494 | C22 | semidirect |
| 15. #19151625 | C22 | semidirect |
| 18. #19151562 | C22 | semidirect |
| 19. #19151554 | C22 | semidirect |
| 20. #19151368 | C22 | semidirect |
| 33. C2×#13083558 | D4 | semidirect |
| 39. C22×#10623494 | D4 | semidirect |
| 152. C89 | #21483 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034964 | 2 |
| #26028947 | 2 |
| #26020671 | 2 |
| #26020540 | 2 |
| #26020203 | 2 |
| #26020054 | 2 |
| C89×#3025 | 2 |
| #21483 | 89 |