Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
352 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26022055 | C2 | semidirect |
| 3. #26018263 | C2 | semidirect |
| 5. C4×#107×C89 | C2 | semidirect |
| 7. #19152000 | C4 | semidirect |
| 8. #19151982 | C4 | semidirect |
| 13. C4×Dic356 | C4 | semidirect |
| 15. C4×D712 | C4 | semidirect |
| 150. C4×#107 | D89 | semidirect |
| 153. C89 | #11746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030822 | 2 |
| #26022055 | 2 |
| #26018263 | 2 |
| #26018260 | 2 |
| C4×#107×C89 | 2 |
| #11746 | 89 |