Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
918 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 918 conjugacy classes of subgroups — too many to draw. Only its 179 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×#19152035 | C2 | semidirect |
| 2. #26030681 | C2 | semidirect |
| 3. #493×D89 | C2 | semidirect |
| 4. #26022517 | C2 | semidirect |
| 5. #26022509 | C2 | semidirect |
| 6. #26022502 | C2 | semidirect |
| 7. #26022501 | C2 | semidirect |
| 8. C4×#15667951 | C2 | semidirect |
| 9. C89×#2248 | C2 | semidirect |
| 17. C2×#15667955 | C22 | semidirect |
| 18. C2×D1424 | C22 | semidirect |
| 19. C2×#15667953 | C22 | semidirect |
| 22. #19151983 | C22 | semidirect |
| 24. #19151975 | C22 | semidirect |
| 30. #19151373 | C22 | semidirect |
| 31. C4×#13083549 | C22 | semidirect |
| 32. C2×SD32×C89 | C22 | semidirect |
| 33. #494×C89 | C22 | semidirect |
| 35. C4×C16×C89 | C22 | semidirect |
| 64. #15667951 | D4 | semidirect |
| 109. #13083549 | C2×D4 | semidirect |
| 121. C16×C89 | C2×D4 | semidirect |
| 166. C4×C89 | #509 | semidirect |
| 183. #2248 | D89 | semidirect |
| 187. C89 | #33717 | semidirect |
| 196. C2×SD32 | C2×D89 | semidirect |
| 202. #494 | C2×D89 | semidirect |
| 213. C4×C16 | C2×D89 | semidirect |
| 299. C16 | D4×D89 | semidirect |
| 346. C4 | #19152035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152035 | 2 |
| #26030681 | 2 |
| #493×D89 | 2 |
| #26022517 | 2 |
| #26022509 | 2 |
| #26022502 | 2 |
| #26022501 | 2 |
| C4×#15667951 | 2 |
| C89×#2248 | 2 |
| #33717 | 89 |