Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
606 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 606 conjugacy classes of subgroups — too many to draw. Only its 93 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. #26018773 | C2 | semidirect |
| 4. #26018771 | C2 | semidirect |
| 6. #26018138 | C2 | semidirect |
| 7. C89×#1297 | C2 | semidirect |
| 11. #19151525 | C4 | semidirect |
| 12. #19151511 | C4 | semidirect |
| 209. #1297 | D89 | semidirect |
| 210. C89 | #9411 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025405 | 2 |
| #26022847 | 2 |
| #26018773 | 2 |
| #26018771 | 2 |
| #26018578 | 2 |
| #26018138 | 2 |
| C89×#1297 | 2 |
| #9411 | 89 |