Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
482 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 482 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. #26018851 | C2 | semidirect |
| 3. #26018605 | C2 | semidirect |
| 4. C8×#13083558 | C2 | semidirect |
| 5. C89×#1568 | C2 | semidirect |
| 147. #1568 | D89 | semidirect |
| 151. C89 | #9787 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151982 | 2 |
| #26018851 | 2 |
| #26018605 | 2 |
| C8×#13083558 | 2 |
| C89×#1568 | 2 |
| #9787 | 89 |