Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1402 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1402 conjugacy classes of subgroups — too many to draw. Only its 183 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. #26031058 | C2 | semidirect |
| 2. #26025410 | C2 | semidirect |
| 3. #26019238 | C2 | semidirect |
| 4. #26019204 | C2 | semidirect |
| 5. #26018768 | C2 | semidirect |
| 6. #26018579 | C2 | semidirect |
| 8. C2×#15667991 | C22 | semidirect |
| 10. #19151909 | C22 | semidirect |
| 13. #19151736 | C22 | semidirect |
| 14. #19151562 | C22 | semidirect |
| 15. #19151523 | C22 | semidirect |
| 16. #19151510 | C22 | semidirect |
| 20. C4×C22⋊Dic89 | C22 | semidirect |
| 21. #19151332 | C22 | semidirect |
| 22. #19151322 | C22 | semidirect |
| 32. C22×Dic178 | C23 | semidirect |
| 37. C2×C4⋊Dic89 | C23 | semidirect |
| 48. C22⋊#10623494 | C23 | semidirect |
| 51. #15667919 | C23 | semidirect |
| 243. C89 | #18317 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031058 | 2 |
| #26025410 | 2 |
| #26019238 | 2 |
| #26019204 | 2 |
| #26018768 | 2 |
| #26018579 | 2 |
| C2×#534×C89 | 2 |
| #18317 | 89 |