Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
686 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26018771 | C2 | semidirect |
| 5. #26018615 | C2 | semidirect |
| 6. #26018129 | C2 | semidirect |
| 7. C89×#1282 | C2 | semidirect |
| 9. C22×Dic356 | C4 | semidirect |
| 10. C22×#13083563 | C4 | semidirect |
| 19. C2×#15667937 | C4 | semidirect |
| 20. C2×#15667934 | C4 | semidirect |
| 278. #1282 | D89 | semidirect |
| 279. C89 | #9239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151762 | 2 |
| #26028698 | 2 |
| #26020197 | 2 |
| #26018771 | 2 |
| #26018615 | 2 |
| #26018129 | 2 |
| C89×#1282 | 2 |
| #9239 | 89 |