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 |
|---|---|---|
| 2. #26030374 | C2 | semidirect |
| 3. #26019373 | C2 | semidirect |
| 4. #26019311 | C2 | semidirect |
| 5. #26018966 | C2 | semidirect |
| 6. #26018699 | C2 | semidirect |
| 7. C2×#559×C89 | C2 | semidirect |
| 14. #19151893 | C22 | semidirect |
| 15. #19151798 | C22 | semidirect |
| 21. Q8⋊#10623494 | C22 | semidirect |
| 165. C2×#559 | D89 | semidirect |
| 172. C89 | #18526 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030702 | 2 |
| #26030374 | 2 |
| #26019373 | 2 |
| #26019311 | 2 |
| #26018966 | 2 |
| #26018699 | 2 |
| C2×#559×C89 | 2 |
| #18526 | 89 |