Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
560 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 95 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. #26020351 | C2 | semidirect |
| 5. #26018138 | C2 | semidirect |
| 6. #26018137 | C2 | semidirect |
| 7. C89×#1826 | C2 | semidirect |
| 15. #19151536 | C4 | semidirect |
| 16. #19151533 | C4 | semidirect |
| 17. #19151529 | C4 | semidirect |
| 19. #19151524 | C4 | semidirect |
| 233. #1826 | D89 | semidirect |
| 237. C89 | #9011 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029279 | 2 |
| #26023509 | 2 |
| #26020351 | 2 |
| C4×#15667926 | 2 |
| #26018138 | 2 |
| #26018137 | 2 |
| C89×#1826 | 2 |
| #9011 | 89 |