Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1068 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 163 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×#19152334 | C2 | semidirect |
| 2. #26030370 | C2 | semidirect |
| 3. #26019371 | C2 | semidirect |
| 4. #26019309 | C2 | semidirect |
| 5. #26018966 | C2 | semidirect |
| 6. #26018700 | C2 | semidirect |
| 16. #19151890 | C22 | semidirect |
| 17. #19151795 | C22 | semidirect |
| 22. #19151330 | C22 | semidirect |
| 172. C89 | #18526 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152334 | 2 |
| #26030370 | 2 |
| #26019371 | 2 |
| #26019309 | 2 |
| #26018966 | 2 |
| #26018700 | 2 |
| C89×#3151 | 2 |
| #18526 | 89 |