Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
612 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 3. #26018825 | C2 | semidirect |
| 4. #26018823 | C2 | semidirect |
| 6. #26018119 | C2 | semidirect |
| 7. C89×#1289 | C2 | semidirect |
| 11. #19151535 | C4 | semidirect |
| 13. #19151511 | C4 | semidirect |
| 235. #1289 | D89 | semidirect |
| 236. C89 | #9201 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26026060 | 2 |
| #26022849 | 2 |
| #26018825 | 2 |
| #26018823 | 2 |
| C2×#19151321 | 2 |
| #26018119 | 2 |
| C89×#1289 | 2 |
| #9201 | 89 |