Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
564 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26023332 | C2 | semidirect |
| 4. #26018823 | C2 | semidirect |
| 6. #26018098 | C2 | semidirect |
| 7. C89×#1294 | C2 | semidirect |
| 10. #19151929 | C4 | semidirect |
| 13. #19151751 | C4 | semidirect |
| 113. C22⋊Dic89 | SD16 | semidirect |
| 249. #1294 | D89 | semidirect |
| 251. C89 | #9278 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031010 | 2 |
| #26023332 | 2 |
| #26021087 | 2 |
| #26018823 | 2 |
| C2×#19151331 | 2 |
| #26018098 | 2 |
| C89×#1294 | 2 |
| #9278 | 89 |