Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1230 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1230 conjugacy classes of subgroups — too many to draw. Only its 183 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. #26031058 | C2 | semidirect |
| 2. #26025632 | C2 | semidirect |
| 3. #26019255 | C2 | semidirect |
| 4. #26019221 | C2 | semidirect |
| 5. #26018768 | C2 | semidirect |
| 6. #26018582 | C2 | semidirect |
| 10. #19151909 | C22 | semidirect |
| 13. #19151736 | C22 | semidirect |
| 15. #19151528 | C22 | semidirect |
| 16. #19151518 | C22 | semidirect |
| 21. #19151332 | C22 | semidirect |
| 22. #19151324 | C22 | semidirect |
| 221. C89 | #18325 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031058 | 2 |
| #26025632 | 2 |
| #26019255 | 2 |
| #26019221 | 2 |
| #26018768 | 2 |
| #26018582 | 2 |
| C2×#537×C89 | 2 |
| #18325 | 89 |