Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
420 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #26020300 | C2 | semidirect |
| 5. #26020296 | C2 | semidirect |
| 6. #26018381 | C2 | semidirect |
| 7. C89×#1395 | C2 | semidirect |
| 9. C22×#13083557 | C4 | semidirect |
| 17. #19151624 | C4 | semidirect |
| 20. #19151561 | C4 | semidirect |
| 21. #19151556 | C4 | semidirect |
| 213. #1395 | D89 | semidirect |
| 214. C89 | #12806 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028958 | 2 |
| #26021894 | 2 |
| #26021891 | 2 |
| #26020300 | 2 |
| #26020296 | 2 |
| #26018381 | 2 |
| C89×#1395 | 2 |
| #12806 | 89 |