Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
580 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 580 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 |
|---|---|---|
| 1. #26029293 | C2 | semidirect |
| 3. #26018767 | C2 | semidirect |
| 4. #26018105 | C2 | semidirect |
| 5. C4×#99×C89 | C2 | semidirect |
| 11. #19151537 | C4 | semidirect |
| 12. #19151534 | C4 | semidirect |
| 13. #19151515 | C4 | semidirect |
| 15. #19151507 | C4 | semidirect |
| 43. C22⋊#10623494 | D4 | semidirect |
| 206. C4×#99 | D89 | semidirect |
| 209. C89 | #9186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029293 | 2 |
| #26026136 | 2 |
| #26018767 | 2 |
| #26018105 | 2 |
| C4×#99×C89 | 2 |
| #9186 | 89 |