Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
732 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26021238 | C2 | semidirect |
| 5. #26018159 | C2 | semidirect |
| 6. #26018138 | C2 | semidirect |
| 7. C89×#1508 | C2 | semidirect |
| 9. C2×#15668043 | C4 | semidirect |
| 15. #19151597 | C4 | semidirect |
| 230. #1508 | D89 | semidirect |
| 233. C89 | #9364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029510 | 2 |
| #26023092 | 2 |
| #26021238 | 2 |
| #26020195 | 2 |
| #26018159 | 2 |
| #26018138 | 2 |
| C89×#1508 | 2 |
| #9364 | 89 |