Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
414 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26018868 | C2 | semidirect |
| 4. #26018817 | C2 | semidirect |
| 6. #26018134 | C2 | semidirect |
| 7. C89×#1302 | C2 | semidirect |
| 10. #19152007 | C4 | semidirect |
| 11. #19151992 | C4 | semidirect |
| 12. #19151967 | C4 | semidirect |
| 13. #19151958 | C4 | semidirect |
| 204. #1302 | D89 | semidirect |
| 206. C89 | #9431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030961 | 2 |
| #26029241 | 2 |
| #26018868 | 2 |
| #26018817 | 2 |
| #26018791 | 2 |
| #26018134 | 2 |
| C89×#1302 | 2 |
| #9431 | 89 |