Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1154 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 351 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. #26028863 | C2 | semidirect |
| 3. #26022002 | C2 | semidirect |
| 4. C2×#19151412 | C2 | semidirect |
| 5. C89×#3407 | C2 | semidirect |
| 14. C2×#15667948 | C22 | semidirect |
| 15. #19151415 | C22 | semidirect |
| 16. #19151412 | C22 | semidirect |
| 19. C2×M32×C89 | C22 | semidirect |
| 117. #3407 | D89 | semidirect |
| 121. C89 | #33392 | semidirect |
| 131. C2×M32 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152403 | 2 |
| #26028863 | 2 |
| #26022002 | 2 |
| C2×#19151412 | 2 |
| C89×#3407 | 2 |
| #33392 | 89 |