Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1068 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 179 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. #26030709 | C2 | semidirect |
| 2. #26030343 | C2 | semidirect |
| 3. #26019397 | C2 | semidirect |
| 4. #26019335 | C2 | semidirect |
| 5. #26018978 | C2 | semidirect |
| 6. #26018695 | C2 | semidirect |
| 7. C2×#555×C89 | C2 | semidirect |
| 11. #19151977 | C22 | semidirect |
| 12. #19151972 | C22 | semidirect |
| 14. #19151888 | C22 | semidirect |
| 15. #19151793 | C22 | semidirect |
| 20. #19151347 | C22 | semidirect |
| 21. D4⋊#10623494 | C22 | semidirect |
| 167. C2×#555 | D89 | semidirect |
| 174. C89 | #18547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030709 | 2 |
| #26030343 | 2 |
| #26019397 | 2 |
| #26019335 | 2 |
| #26018978 | 2 |
| #26018695 | 2 |
| C2×#555×C89 | 2 |
| #18547 | 89 |