Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
390 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 390 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 |
|---|---|---|
| 4. #26018804 | C2 | semidirect |
| 5. #26018672 | C2 | semidirect |
| 6. #26018118 | C2 | semidirect |
| 7. C89×#1287 | C2 | semidirect |
| 10. #19152007 | C4 | semidirect |
| 11. #19152007 | C4 | semidirect |
| 12. #19151958 | C4 | semidirect |
| 13. #19151958 | C4 | semidirect |
| 196. #1287 | D89 | semidirect |
| 197. C89 | #9369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031494 | 2 |
| #26029232 | 2 |
| #26018830 | 2 |
| #26018804 | 2 |
| #26018672 | 2 |
| #26018118 | 2 |
| C89×#1287 | 2 |
| #9369 | 89 |