Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
290 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 290 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. #19151622 | C4 | semidirect |
| 8. C42×Dic89 | C4 | semidirect |
| 10. #19151391 | C4 | semidirect |
| 13. #356×C89 | C4 | semidirect |
| 123. C89 | #7497 | semidirect |
| 131. #356 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021917 | 2 |
| #26021081 | 2 |
| C89×#2132 | 2 |
| #7497 | 89 |