Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
566 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 85 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. #26031438 | C2 | semidirect |
| 2. #26025418 | C2 | semidirect |
| 3. #26021172 | C2 | semidirect |
| 4. #26018855 | C2 | semidirect |
| 5. #26018695 | C2 | semidirect |
| 6. #26018107 | C2 | semidirect |
| 224. C89 | #10005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031438 | 2 |
| #26025418 | 2 |
| #26021172 | 2 |
| #26018855 | 2 |
| #26018695 | 2 |
| #26018107 | 2 |
| C89×#3109 | 2 |
| #10005 | 89 |