Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
508 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 101 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. #26018131 | C2 | semidirect |
| 5. #26018119 | C2 | semidirect |
| 6. #26018100 | C2 | semidirect |
| 7. C89×#2549 | C2 | semidirect |
| 27. C22×D356 | Q8 | semidirect |
| 36. C2×C4⋊Dic89 | Q8 | semidirect |
| 230. #2549 | D89 | semidirect |
| 237. C89 | #10374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021088 | 2 |
| #26018819 | 2 |
| C2×#19151331 | 2 |
| #26018131 | 2 |
| #26018119 | 2 |
| #26018100 | 2 |
| C89×#2549 | 2 |
| #10374 | 89 |