Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
716 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 716 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 |
|---|---|---|
| 1. #26031024 | C2 | semidirect |
| 5. #26018615 | C2 | semidirect |
| 6. #26018128 | C2 | semidirect |
| 7. C89×#1472 | C2 | semidirect |
| 243. #1472 | D89 | semidirect |
| 245. C89 | #9976 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031024 | 2 |
| #26029514 | 2 |
| #26029510 | 2 |
| #26020163 | 2 |
| #26018615 | 2 |
| #26018128 | 2 |
| C89×#1472 | 2 |
| #9976 | 89 |