Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
408 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 408 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. #26020472 | C2 | semidirect |
| 5. #26018382 | C2 | semidirect |
| 6. #26018381 | C2 | semidirect |
| 7. C89×#1858 | C2 | semidirect |
| 20. #19151396 | C4 | semidirect |
| 21. #19151394 | C4 | semidirect |
| 192. #1858 | D89 | semidirect |
| 195. C89 | #12974 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029321 | 2 |
| #26021935 | 2 |
| #26020635 | 2 |
| #26020472 | 2 |
| #26018382 | 2 |
| #26018381 | 2 |
| C89×#1858 | 2 |
| #12974 | 89 |