Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
272 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 79 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. #26022532 | C2 | semidirect |
| 4. #26019869 | C2 | semidirect |
| 6. #26018171 | C2 | semidirect |
| 7. C89×#2254 | C2 | semidirect |
| 102. #2254 | D89 | semidirect |
| 108. C89 | #12532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022532 | 2 |
| #26022477 | 2 |
| #26022476 | 2 |
| #26019869 | 2 |
| #26019845 | 2 |
| #26018171 | 2 |
| C89×#2254 | 2 |
| #12532 | 89 |