Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1380 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 1380 conjugacy classes of subgroups — too many to draw. Only its 211 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. C2×#19152034 | C2 | semidirect |
| 2. #26029833 | C2 | semidirect |
| 3. #26022181 | C2 | semidirect |
| 4. #26022164 | C2 | semidirect |
| 5. #26021968 | C2 | semidirect |
| 6. #26021863 | C2 | semidirect |
| 7. C23×D8×C89 | C2 | semidirect |
| 8. C2×#15668034 | C22 | semidirect |
| 11. C2×#15667956 | C22 | semidirect |
| 12. C2×#15667953 | C22 | semidirect |
| 13. C2×#15667952 | C22 | semidirect |
| 14. #19151839 | C22 | semidirect |
| 15. #19151834 | C22 | semidirect |
| 17. #19151636 | C22 | semidirect |
| 19. #19151399 | C22 | semidirect |
| 20. C22⋊#13083549 | C22 | semidirect |
| 30. C2×Dic356 | C23 | semidirect |
| 32. C2×D712 | C23 | semidirect |
| 42. C2×#13083549 | C23 | semidirect |
| 43. #15667946 | C23 | semidirect |
| 61. C2×D8×C89 | D4 | semidirect |
| 162. C22×C89 | #509 | semidirect |
| 179. C23×D8 | D89 | semidirect |
| 186. C89 | #33517 | semidirect |
| 226. C2×D8 | C22⋊D89 | semidirect |
| 343. C22 | #19152034 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152034 | 2 |
| #26029833 | 2 |
| #26022181 | 2 |
| #26022164 | 2 |
| #26021968 | 2 |
| #26021863 | 2 |
| C23×D8×C89 | 2 |
| #33517 | 89 |