Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1450 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 1450 conjugacy classes of subgroups — too many to draw. Only its 167 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×#19152179 | C2 | semidirect |
| 2. #26029504 | C2 | semidirect |
| 3. #26019220 | C2 | semidirect |
| 4. #26019186 | C2 | semidirect |
| 5. #26018780 | C2 | semidirect |
| 6. #26018582 | C2 | semidirect |
| 7. C89×#2406 | C2 | semidirect |
| 18. #19151737 | C22 | semidirect |
| 19. #19151732 | C22 | semidirect |
| 22. #19151331 | C22 | semidirect |
| 23. #19151324 | C22 | semidirect |
| 27. #395×C89 | C22 | semidirect |
| 28. #394×C89 | C22 | semidirect |
| 193. C2×C4×C89 | AGL(1,ℤ/8) | semidirect |
| 244. #2406 | D89 | semidirect |
| 249. C89 | #18142 | semidirect |
| 267. #395 | C2×D89 | semidirect |
| 268. #394 | C2×D89 | semidirect |
| 445. C2×C4 | #15668037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152179 | 2 |
| #26029504 | 2 |
| #26019220 | 2 |
| #26019186 | 2 |
| #26018780 | 2 |
| #26018582 | 2 |
| C89×#2406 | 2 |
| #18142 | 89 |