Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
746 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 746 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 3. #26018950 | C2 | semidirect |
| 4. #26018868 | C2 | semidirect |
| 5. #26018867 | C2 | semidirect |
| 7. C89×#1552 | C2 | semidirect |
| 218. #1552 | D89 | semidirect |
| 222. C89 | #8457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034053 | 2 |
| #26021049 | 2 |
| #26018950 | 2 |
| #26018868 | 2 |
| #26018867 | 2 |
| #26018592 | 2 |
| C89×#1552 | 2 |
| #8457 | 89 |