Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
478 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. #26021229 | C2 | semidirect |
| 5. #26018672 | C2 | semidirect |
| 6. #26018143 | C2 | semidirect |
| 7. C89×#1276 | C2 | semidirect |
| 11. #19151884 | C4 | semidirect |
| 12. #19151879 | C4 | semidirect |
| 13. #19151809 | C4 | semidirect |
| 14. #19151804 | C4 | semidirect |
| 212. #1276 | D89 | semidirect |
| 213. C89 | #8971 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030324 | 2 |
| #26029373 | 2 |
| #26021229 | 2 |
| C4×#15667940 | 2 |
| #26018672 | 2 |
| #26018143 | 2 |
| C89×#1276 | 2 |
| #8971 | 89 |