Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
416 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 59 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. #26021914 | C2 | semidirect |
| 3. #26018417 | C2 | semidirect |
| 4. #26018414 | C2 | semidirect |
| 5. C89×#1409 | C2 | semidirect |
| 7. #19152149 | C4 | semidirect |
| 10. #19151977 | C4 | semidirect |
| 12. #19151971 | C4 | semidirect |
| 14. C4×C8×D89 | C4 | semidirect |
| 134. #1409 | D89 | semidirect |
| 136. C89 | #13583 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030675 | 2 |
| #26021914 | 2 |
| #26018417 | 2 |
| #26018414 | 2 |
| C89×#1409 | 2 |
| #13583 | 89 |