Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
468 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 468 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. #26021923 | C2 | semidirect |
| 3. #26021902 | C2 | semidirect |
| 4. #26021901 | C2 | semidirect |
| 5. #26020296 | C2 | semidirect |
| 6. #26020054 | C2 | semidirect |
| 7. C89×#2128 | C2 | semidirect |
| 8. C22×#13083559 | C4 | semidirect |
| 16. #19151634 | C4 | semidirect |
| 17. #19151603 | C4 | semidirect |
| 18. #19151602 | C4 | semidirect |
| 222. #2128 | D89 | semidirect |
| 227. C89 | #13231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029897 | 2 |
| #26021923 | 2 |
| #26021902 | 2 |
| #26021901 | 2 |
| #26020296 | 2 |
| #26020054 | 2 |
| C89×#2128 | 2 |
| #13231 | 89 |