Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
296 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 2. #26022479 | C2 | semidirect |
| 4. #26018311 | C2 | semidirect |
| 5. Q8⋊#13083549 | C2 | semidirect |
| 7. C89×#1670 | C2 | semidirect |
| 129. #1670 | D89 | semidirect |
| 133. C89 | #12359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033120 | 2 |
| #26022479 | 2 |
| #26022294 | 2 |
| #26018311 | 2 |
| Q8⋊#13083549 | 2 |
| #26018212 | 2 |
| C89×#1670 | 2 |
| #12359 | 89 |