Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
296 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 83 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. #26020425 | C2 | semidirect |
| 5. #26018363 | C2 | semidirect |
| 6. #26018331 | C2 | semidirect |
| 7. C89×#1388 | C2 | semidirect |
| 143. #1388 | D89 | semidirect |
| 145. C89 | #13486 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022002 | 2 |
| #26021999 | 2 |
| #26021143 | 2 |
| #26020425 | 2 |
| #26018363 | 2 |
| #26018331 | 2 |
| C89×#1388 | 2 |
| #13486 | 89 |