Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
852 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 87 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. #26031059 | C2 | semidirect |
| 2. C2×#19151749 | C2 | semidirect |
| 4. #26018617 | C2 | semidirect |
| 5. #26018613 | C2 | semidirect |
| 6. #26018139 | C2 | semidirect |
| 7. C89×#1783 | C2 | semidirect |
| 235. #1783 | D89 | semidirect |
| 239. C89 | #9987 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031059 | 2 |
| C2×#19151749 | 2 |
| C2×#19151732 | 2 |
| #26018617 | 2 |
| #26018613 | 2 |
| #26018139 | 2 |
| C89×#1783 | 2 |
| #9987 | 89 |