Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
348 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 63 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. #19152073 | C4 | semidirect |
| 7. C2×#15667929 | C4 | semidirect |
| 10. #19151342 | C4 | semidirect |
| 14. #353×C89 | C4 | semidirect |
| 144. C89 | #7485 | semidirect |
| 152. #353 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020651 | 2 |
| C2×#19151342 | 2 |
| C2×#353×C89 | 2 |
| #7485 | 89 |