Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
424 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 424 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. #26020540 | C2 | semidirect |
| 5. #26020537 | C2 | semidirect |
| 6. #26018372 | C2 | semidirect |
| 7. C89×#1391 | C2 | semidirect |
| 21. #19151392 | C4 | semidirect |
| 22. #19151390 | C4 | semidirect |
| 196. #1391 | D89 | semidirect |
| 197. C89 | #12968 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029316 | 2 |
| #26021915 | 2 |
| #26020633 | 2 |
| #26020540 | 2 |
| #26020537 | 2 |
| #26018372 | 2 |
| C89×#1391 | 2 |
| #12968 | 89 |