Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1372 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1372 conjugacy classes of subgroups — too many to draw. Only its 203 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. C2×#19152229 | C2 | semidirect |
| 4. #26019194 | C2 | direct (N × H) |
| 5. C2×#19151336 | C2 | semidirect |
| 6. C2×#324×C89 | C2 | semidirect |
| 11. #19152229 | C22 | semidirect |
| 25. #19151336 | C22 | semidirect |
| 28. #324×C89 | C22 | semidirect |
| 126. C22×C4×C89 | SD16 | semidirect |
| 174. C2×C4×C89 | C2×SD16 | semidirect |
| 224. C2×C89 | #1599 | semidirect |
| 234. C2×#324 | D89 | semidirect |
| 235. C89 | C2×#1599 | semidirect |
| 257. #324 | C2×D89 | semidirect |
| 341. C22×C4 | #13083563 | semidirect |
| 417. C2×C4 | C2×#13083563 | semidirect |
| 453. C2 | #26019194 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152229 | 2 |
| C2×#19151751 | 2 |
| C2×#19151515 | 2 |
| #26019194 | 2 |
| C2×#19151336 | 2 |
| C2×#324×C89 | 2 |
| C2×#1599 | 89 |