Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
472 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 472 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 |
|---|---|---|
| 4. #26018132 | C2 | semidirect |
| 5. #26018130 | C2 | semidirect |
| 6. #26018119 | C2 | semidirect |
| 7. C89×#1289 | C2 | semidirect |
| 14. #19151465 | C4 | semidirect |
| 15. #19151460 | C4 | semidirect |
| 18. #19151445 | C4 | semidirect |
| 19. #19151443 | C4 | semidirect |
| 234. #1289 | D89 | semidirect |
| 235. C89 | #8763 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023194 | 2 |
| #26020237 | 2 |
| #26018568 | 2 |
| #26018132 | 2 |
| #26018130 | 2 |
| #26018119 | 2 |
| C89×#1289 | 2 |
| #8763 | 89 |