Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
452 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 87 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. #26021926 | C2 | semidirect |
| 4. #26021907 | C2 | semidirect |
| 5. #26020296 | C2 | semidirect |
| 6. #26020055 | C2 | semidirect |
| 8. C22×#13083562 | C4 | semidirect |
| 16. #19151634 | C4 | semidirect |
| 17. #19151606 | C4 | semidirect |
| 18. #19151603 | C4 | semidirect |
| 220. C89 | #13229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029888 | 2 |
| #26021926 | 2 |
| #26021924 | 2 |
| #26021907 | 2 |
| #26020296 | 2 |
| #26020055 | 2 |
| C89×#2122 | 2 |
| #13229 | 89 |