Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
464 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 93 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. #26020457 | C2 | semidirect |
| 5. #26018138 | C2 | semidirect |
| 6. #26018099 | C2 | semidirect |
| 7. C89×#1851 | C2 | semidirect |
| 22. #19151334 | C4 | semidirect |
| 23. #19151334 | C4 | semidirect |
| 24. #19151331 | C4 | semidirect |
| 25. #19151331 | C4 | semidirect |
| 221. #1851 | D89 | semidirect |
| 225. C89 | #8874 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029297 | 2 |
| #26020554 | 2 |
| #26020457 | 2 |
| #26018741 | 2 |
| #26018138 | 2 |
| #26018099 | 2 |
| C89×#1851 | 2 |
| #8874 | 89 |