Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
584 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 171 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. C2×#19151636 | C2 | semidirect |
| 2. #26022457 | C2 | semidirect |
| 3. #26022440 | C2 | semidirect |
| 4. #26022041 | C2 | semidirect |
| 5. #26021964 | C2 | semidirect |
| 6. #26021863 | C2 | semidirect |
| 14. #19151425 | C22 | semidirect |
| 15. #19151423 | C22 | semidirect |
| 16. #19151402 | C22 | semidirect |
| 17. #19151399 | C22 | semidirect |
| 151. C89 | #33647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151636 | 2 |
| #26022457 | 2 |
| #26022440 | 2 |
| #26022041 | 2 |
| #26021964 | 2 |
| #26021863 | 2 |
| C89×#3050 | 2 |
| #33647 | 89 |