Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
624 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26021946 | C2 | semidirect |
| 4. #26021907 | C2 | semidirect |
| 6. #26018381 | C2 | semidirect |
| 7. C89×#1392 | C2 | semidirect |
| 9. C2×#15668045 | C4 | semidirect |
| 10. C22×Dic356 | C4 | semidirect |
| 19. #19151608 | C4 | semidirect |
| 20. #19151595 | C4 | semidirect |
| 245. #1392 | D89 | semidirect |
| 246. C89 | #13096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029549 | 2 |
| #26028733 | 2 |
| #26021946 | 2 |
| #26021907 | 2 |
| #26020228 | 2 |
| #26018381 | 2 |
| C89×#1392 | 2 |
| #13096 | 89 |