Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
480 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 95 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. #26018137 | C2 | semidirect |
| 4. #26018106 | C2 | semidirect |
| 10. #19151466 | C4 | semidirect |
| 12. #19151458 | C4 | semidirect |
| 16. #19151444 | C4 | semidirect |
| 17. C2×#15667919 | C4 | semidirect |
| 179. C89 | #8777 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023192 | 2 |
| C4×#15667927 | 2 |
| #26018137 | 2 |
| #26018106 | 2 |
| C89×#1465 | 2 |
| #8777 | 89 |