Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
290 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 2. #26022455 | C2 | semidirect |
| 4. #26021757 | C2 | semidirect |
| 5. #26018271 | C2 | semidirect |
| 7. C89×#1323 | C2 | semidirect |
| 149. #1323 | D89 | semidirect |
| 150. C89 | #12297 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031713 | 2 |
| #26022455 | 2 |
| #26022433 | 2 |
| #26021757 | 2 |
| #26018271 | 2 |
| #26018268 | 2 |
| C89×#1323 | 2 |
| #12297 | 89 |