Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
284 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
| 3. #26022481 | C2 | semidirect |
| 5. #26019849 | C2 | semidirect |
| 6. C8×#13083549 | C2 | semidirect |
| 54. #13083549 | SD16 | semidirect |
| 85. C8×C89 | SD32 | semidirect |
| 111. C89 | #12505 | semidirect |
| 189. C8 | #15667956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022532 | 2 |
| #26022507 | 2 |
| #26022481 | 2 |
| #26022475 | 2 |
| #26019849 | 2 |
| C8×#13083549 | 2 |
| C89×#1706 | 2 |
| #12505 | 89 |