Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
274 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 4. #19152365 | C4 | semidirect |
| 7. #19151572 | C4 | semidirect |
| 9. #19151347 | C4 | semidirect |
| 13. #354×C89 | C4 | semidirect |
| 121. C89 | #7490 | semidirect |
| 128. #354 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020636 | 2 |
| #26018914 | 2 |
| C89×#2126 | 2 |
| #7490 | 89 |