Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
7034 conjugacy classes of subgroups; only the 675 normal subgroups are shown.
This group has 7034 conjugacy classes of subgroups — too many to draw. Only its 675 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 |
|---|---|---|
| 1. C25×Dic89 | C2 | semidirect |
| 3. C2×#19151475 | C2 | semidirect |
| 4. #26018474 | C2 | semidirect |
| 5. C2×#379×C89 | C2 | semidirect |
| 12. C2×#15667981 | C4 | semidirect |
| 14. C22×#13083551 | C22 | semidirect |
| 16. C2×#15667919 | C22 | semidirect |
| 25. C22×C22⋊D89 | C2×C4 | semidirect |
| 31. C23×Dic89 | D4 | semidirect |
| 37. C2×C22⋊Dic89 | C2×C4 | semidirect |
| 54. C23×D89 | C22×C4 | semidirect |
| 71. C22×Dic89 | C22×C4 | semidirect |
| 83. C24×C89 | C22⋊C4 | semidirect |
| 135. C2×Dic89 | #120 | semidirect |
| 143. C22×C89 | #386 | semidirect |
| 170. C2×#379 | D89 | semidirect |
| 172. C89 | #14694 | semidirect |
| 230. C24 | #13083551 | semidirect |
| 315. C22 | #19151475 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×Dic89 | 2 |
| C22×#15667981 | 2 |
| C2×#19151475 | 2 |
| #26018474 | 2 |
| C2×#379×C89 | 2 |
| #14694 | 89 |