Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
566 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. #26023543 | C2 | semidirect |
| 5. #26018680 | C2 | semidirect |
| 6. #26018080 | C2 | semidirect |
| 7. C89×#1487 | C2 | semidirect |
| 113. C4×Dic89 | SD16 | semidirect |
| 210. #1487 | D89 | semidirect |
| 212. C89 | #10014 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030284 | 2 |
| #26030283 | 2 |
| #26023543 | 2 |
| #26021083 | 2 |
| #26018680 | 2 |
| #26018080 | 2 |
| C89×#1487 | 2 |
| #10014 | 89 |