Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
412 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26019043 | C2 | semidirect |
| 5. #26018084 | C2 | semidirect |
| 6. #26018084 | C2 | semidirect |
| 7. C89×#1574 | C2 | semidirect |
| 20. #19151346 | C4 | semidirect |
| 21. #19151346 | C4 | semidirect |
| 22. #19151341 | C4 | semidirect |
| 23. #19151341 | C4 | semidirect |
| 166. #1574 | D89 | semidirect |
| 170. C89 | #8934 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029318 | 2 |
| #26021079 | 2 |
| #26019043 | 2 |
| #26018912 | 2 |
| #26018084 | 2 |
| C89×#1574 | 2 |
| #8934 | 89 |