Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
762 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 762 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26022865 | C2 | semidirect |
| 3. #26018821 | C2 | semidirect |
| 4. #26018819 | C2 | semidirect |
| 5. C2×#19151321 | C2 | semidirect |
| 6. #26018119 | C2 | semidirect |
| 7. C89×#1289 | C2 | semidirect |
| 13. #19151525 | C4 | semidirect |
| 15. #19151508 | C4 | semidirect |
| 29. C22×D356 | C2×C4 | semidirect |
| 41. C2×C4⋊Dic89 | C2×C4 | semidirect |
| 60. #15667919 | D4 | semidirect |
| 69. #95×C89 | C2×C4 | semidirect |
| 70. #95×C89 | D4 | semidirect |
| 262. #1289 | D89 | semidirect |
| 263. C89 | #9203 | semidirect |
| 325. #95 | C4×D89 | semidirect |
| 326. #95 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025989 | 2 |
| #26022865 | 2 |
| #26018821 | 2 |
| #26018819 | 2 |
| C2×#19151321 | 2 |
| #26018119 | 2 |
| C89×#1289 | 2 |
| #9203 | 89 |