Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
420 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. #26020300 | C2 | semidirect |
| 4. #26020296 | C2 | semidirect |
| 5. #26018382 | C2 | semidirect |
| 6. #26018380 | C2 | semidirect |
| 9. C22×#13083558 | C4 | semidirect |
| 16. #19151625 | C4 | semidirect |
| 20. #19151562 | C4 | semidirect |
| 21. #19151554 | C4 | semidirect |
| 214. C89 | #12806 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028956 | 2 |
| #26021893 | 2 |
| #26020300 | 2 |
| #26020296 | 2 |
| #26018382 | 2 |
| #26018380 | 2 |
| C89×#2120 | 2 |
| #12806 | 89 |