Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
402 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 85 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. #26029357 | C2 | semidirect |
| 4. #26018804 | C2 | semidirect |
| 6. #26018117 | C2 | semidirect |
| 7. C89×#1291 | C2 | semidirect |
| 10. #19152003 | C4 | semidirect |
| 11. #19151971 | C4 | semidirect |
| 12. #19151949 | C4 | semidirect |
| 13. #19151945 | C4 | semidirect |
| 161. #1291 | D89 | semidirect |
| 163. C89 | #9418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030970 | 2 |
| #26029357 | 2 |
| #26018886 | 2 |
| #26018804 | 2 |
| #26018800 | 2 |
| #26018117 | 2 |
| C89×#1291 | 2 |
| #9418 | 89 |