Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
726 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26022837 | C2 | semidirect |
| 3. #26020175 | C2 | semidirect |
| 6. #26018105 | C2 | semidirect |
| 7. C89×#1284 | C2 | semidirect |
| 9. C2×#15668000 | C4 | semidirect |
| 15. #19151504 | C4 | semidirect |
| 219. #1284 | D89 | semidirect |
| 220. C89 | #9466 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023910 | 2 |
| #26022837 | 2 |
| #26020175 | 2 |
| #26018782 | 2 |
| #26018780 | 2 |
| #26018105 | 2 |
| C89×#1284 | 2 |
| #9466 | 89 |