Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1006 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1006 conjugacy classes of subgroups — too many to draw. Only its 163 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. #26034596 | C2 | semidirect |
| 2. #26031270 | C2 | semidirect |
| 3. #26019333 | C2 | semidirect |
| 4. #26019328 | C2 | semidirect |
| 5. #26019321 | C2 | semidirect |
| 6. #26018978 | C2 | semidirect |
| 7. #26018713 | C2 | semidirect |
| 8. C2×#492×C89 | C2 | semidirect |
| 10. #19152328 | C22 | semidirect |
| 11. #19152314 | C22 | semidirect |
| 12. #19152309 | C22 | semidirect |
| 26. #19151347 | C22 | semidirect |
| 27. #19151347 | C22 | semidirect |
| 28. #19151330 | C22 | semidirect |
| 29. #19151327 | C22 | semidirect |
| 207. C2×#492 | D89 | semidirect |
| 213. C89 | #18684 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034596 | 2 |
| #26031270 | 2 |
| #26019333 | 2 |
| #26019328 | 2 |
| #26019321 | 2 |
| #26018978 | 2 |
| #26018713 | 2 |
| C2×#492×C89 | 2 |
| #18684 | 89 |