Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
234 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 67 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. #26018316 | C2 | semidirect |
| 5. #26018307 | C2 | semidirect |
| 6. #26018301 | C2 | semidirect |
| 7. C89×#1707 | C2 | semidirect |
| 111. #1707 | D89 | semidirect |
| 116. C89 | #12422 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022386 | 2 |
| #26022294 | 2 |
| C8×D712 | 2 |
| #26018316 | 2 |
| #26018307 | 2 |
| #26018301 | 2 |
| C89×#1707 | 2 |
| #12422 | 89 |