Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
786 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 2. C4×#15667927 | C2 | semidirect |
| 3. #26018250 | C2 | semidirect |
| 4. C89×#1466 | C2 | semidirect |
| 5. C23×D356 | C4 | semidirect |
| 9. #19151515 | C4 | semidirect |
| 12. #19151458 | C4 | semidirect |
| 15. #19151365 | C22 | semidirect |
| 19. #323×C89 | C22 | semidirect |
| 195. #1466 | D89 | semidirect |
| 197. C89 | #11772 | semidirect |
| 212. #323 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023608 | 2 |
| C4×#15667927 | 2 |
| #26018250 | 2 |
| C89×#1466 | 2 |
| #11772 | 89 |