Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1538 conjugacy classes of subgroups; only the 297 normal subgroups are shown.
This group has 1538 conjugacy classes of subgroups — too many to draw. Only its 297 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 |
|---|---|---|
| 2. #123×Dic89 | C2 | semidirect |
| 3. #26020666 | C2 | semidirect |
| 4. #26020535 | C2 | semidirect |
| 6. #99×Dic89 | C2 | semidirect |
| 14. C22×C4×Dic89 | C22 | semidirect |
| 19. #19151473 | C22 | semidirect |
| 20. #19151461 | C22 | semidirect |
| 23. C22⋊C4×Dic89 | C22 | semidirect |
| 24. #19151364 | C22 | semidirect |
| 27. #458×C89 | C4 | semidirect |
| 71. #123×C89 | C2×C4 | semidirect |
| 75. #99×C89 | C2×C4 | semidirect |
| 122. C22×C4×C89 | C22×C4 | semidirect |
| 127. C22⋊C4×C89 | C22×C4 | semidirect |
| 194. Dic89 | #458 | direct (N × H) |
| 209. C89 | C4×#458 | semidirect |
| 219. #458 | Dic89 | direct (N × H) |
| 242. #123 | C2×Dic89 | semidirect |
| 272. #99 | C2×Dic89 | semidirect |
| 309. C22×C4 | C22×Dic89 | semidirect |
| 323. C22⋊C4 | C22×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(5,𝔽2)×Dic89 | 2 |
| #123×Dic89 | 2 |
| #26020666 | 2 |
| #26020535 | 2 |
| #26020200 | 2 |
| #99×Dic89 | 2 |
| C2×#458×C89 | 2 |
| C4×#458 | 89 |