Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
616 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26018960 | C2 | semidirect |
| 5. #26018804 | C2 | semidirect |
| 6. #26018803 | C2 | semidirect |
| 7. C89×#1497 | C2 | semidirect |
| 9. #19152328 | C4 | semidirect |
| 11. #19152323 | C4 | semidirect |
| 12. #19152322 | C4 | semidirect |
| 15. #19152309 | C4 | semidirect |
| 257. #1497 | D89 | semidirect |
| 258. C89 | #8501 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034734 | 2 |
| #26018960 | 2 |
| #26018881 | 2 |
| #26018830 | 2 |
| #26018804 | 2 |
| #26018803 | 2 |
| C89×#1497 | 2 |
| #8501 | 89 |