Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
310 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 4. #26018235 | C2 | semidirect |
| 5. #26018234 | C2 | semidirect |
| 6. #26018233 | C2 | semidirect |
| 7. C89×#1338 | C2 | semidirect |
| 151. #1338 | D89 | semidirect |
| 152. C89 | #11642 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #446×D89 | 2 |
| #26022053 | 2 |
| #26022050 | 2 |
| #26018235 | 2 |
| #26018234 | 2 |
| #26018233 | 2 |
| C89×#1338 | 2 |
| #11642 | 89 |