Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
460 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 73 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. #26018274 | C2 | semidirect |
| 5. #26018273 | C2 | semidirect |
| 6. #26018272 | C2 | semidirect |
| 7. C89×#1351 | C2 | semidirect |
| 8. C2×#15668010 | C4 | semidirect |
| 12. #19151511 | C4 | semidirect |
| 14. #19151509 | C4 | semidirect |
| 19. #19151449 | C4 | semidirect |
| 208. #1351 | D89 | semidirect |
| 209. C89 | #11787 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025420 | 2 |
| #26020039 | 2 |
| #26018587 | 2 |
| #26018274 | 2 |
| #26018273 | 2 |
| #26018272 | 2 |
| C89×#1351 | 2 |
| #11787 | 89 |