Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
588 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 111 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. #26022713 | C2 | semidirect |
| 3. #26021081 | C2 | semidirect |
| 4. #26018678 | C2 | semidirect |
| 5. #26018155 | C2 | semidirect |
| 6. #26018084 | C2 | semidirect |
| 7. C89×#1502 | C2 | semidirect |
| 11. #19151875 | C4 | semidirect |
| 12. #19151790 | C4 | semidirect |
| 104. C4×Dic89 | D8 | semidirect |
| 220. #1502 | D89 | semidirect |
| 224. C89 | #9237 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030248 | 2 |
| #26022713 | 2 |
| #26021081 | 2 |
| #26018678 | 2 |
| #26018155 | 2 |
| #26018084 | 2 |
| C89×#1502 | 2 |
| #9237 | 89 |