Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
574 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 574 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. #26022617 | C2 | semidirect |
| 5. #26018146 | C2 | semidirect |
| 6. #26018107 | C2 | semidirect |
| 7. C89×#1491 | C2 | semidirect |
| 11. #19151893 | C4 | semidirect |
| 12. #19151798 | C4 | semidirect |
| 121. Q8×C89 | #104 | semidirect |
| 188. #1491 | D89 | semidirect |
| 191. C89 | #9326 | semidirect |
| 306. Q8 | #15667938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030374 | 2 |
| #26022617 | 2 |
| #26021171 | 2 |
| #26018761 | 2 |
| #26018146 | 2 |
| #26018107 | 2 |
| C89×#1491 | 2 |
| #9326 | 89 |