Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
552 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 83 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. #26019983 | C2 | semidirect |
| 3. #26018563 | C2 | semidirect |
| 4. #26018253 | C2 | semidirect |
| 5. #26018251 | C2 | semidirect |
| 9. C2×D4×Dic89 | C4 | semidirect |
| 13. #19151530 | C4 | semidirect |
| 17. #19151512 | C4 | semidirect |
| 18. #19151449 | C4 | semidirect |
| 223. C89 | #11691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023487 | 2 |
| #26019983 | 2 |
| #26018563 | 2 |
| #26018253 | 2 |
| #26018251 | 2 |
| #26018249 | 2 |
| C89×#1343 | 2 |
| #11691 | 89 |