Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
550 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 71 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. C2×#19151391 | C2 | semidirect |
| 3. #26018398 | C2 | semidirect |
| 4. C89×#1555 | C2 | semidirect |
| 5. C2×#15668057 | C4 | semidirect |
| 9. #19151765 | C4 | semidirect |
| 12. C2×#15667929 | C4 | semidirect |
| 15. #19151391 | C22 | semidirect |
| 19. #331×C89 | C22 | semidirect |
| 23. #15668057 | C2×C4 | semidirect |
| 38. #15667929 | C2×C4 | semidirect |
| 194. #1555 | D89 | semidirect |
| 196. C89 | #13561 | semidirect |
| 211. #331 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151765 | 2 |
| C2×#19151391 | 2 |
| #26018398 | 2 |
| C89×#1555 | 2 |
| #13561 | 89 |