Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
914 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 914 conjugacy classes of subgroups — too many to draw. Only its 135 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. #26022002 | C2 | semidirect |
| 3. #26021981 | C2 | semidirect |
| 4. #26020294 | C2 | semidirect |
| 5. C2×#349×C89 | C2 | semidirect |
| 14. C2×#15667948 | C22 | semidirect |
| 15. C2×#15667948 | C22 | semidirect |
| 22. C2×M32×C89 | C22 | semidirect |
| 196. C2×#349 | D89 | semidirect |
| 198. C89 | #12740 | semidirect |
| 208. C2×M32 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152398 | 2 |
| #26022002 | 2 |
| #26021981 | 2 |
| #26020294 | 2 |
| C2×#349×C89 | 2 |
| #12740 | 89 |