Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
426 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 119 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. #26022055 | C2 | semidirect |
| 2. #26019008 | C2 | semidirect |
| 3. #26018219 | C2 | semidirect |
| 8. #19151374 | C22 | semidirect |
| 10. #19151349 | C22 | semidirect |
| 63. D8×C89 | M16 | semidirect |
| 131. C89 | #11663 | semidirect |
| 187. D8 | #13083558 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022055 | 2 |
| #26019008 | 2 |
| #26018219 | 2 |
| C2×C4×D8×C89 | 2 |
| #11663 | 89 |