Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
448 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26021946 | C2 | semidirect |
| 4. #26021905 | C2 | semidirect |
| 6. #26020302 | C2 | semidirect |
| 7. C89×#1757 | C2 | semidirect |
| 8. C22×#13083563 | C4 | semidirect |
| 16. #19151636 | C4 | semidirect |
| 17. #19151608 | C4 | semidirect |
| 18. #19151604 | C4 | semidirect |
| 217. #1757 | D89 | semidirect |
| 218. C89 | #13232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029891 | 2 |
| #26021946 | 2 |
| #26021943 | 2 |
| #26021905 | 2 |
| #26021901 | 2 |
| #26020302 | 2 |
| C89×#1757 | 2 |
| #13232 | 89 |