Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
712 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 139 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. #26031936 | C2 | semidirect |
| 3. #26022362 | C2 | semidirect |
| 4. #26022304 | C2 | semidirect |
| 5. #26022191 | C2 | semidirect |
| 6. #26022162 | C2 | semidirect |
| 7. C4×D1424 | C2 | semidirect |
| 8. #26022085 | C2 | semidirect |
| 9. C89×#2249 | C2 | semidirect |
| 11. C2×D8×D89 | C22 | semidirect |
| 14. C2×#15667955 | C22 | semidirect |
| 17. C2×#15667951 | C22 | semidirect |
| 18. #19151836 | C22 | semidirect |
| 23. C4×D712 | C22 | semidirect |
| 25. #19151424 | C22 | semidirect |
| 26. C4⋊#13083549 | C22 | semidirect |
| 27. #19151402 | C22 | semidirect |
| 28. #19151400 | C22 | semidirect |
| 29. #19151399 | C22 | semidirect |
| 30. #19151377 | C22 | semidirect |
| 31. C2×Q32×C89 | C22 | semidirect |
| 32. C2×SD32×C89 | C22 | semidirect |
| 34. #495×C89 | C22 | semidirect |
| 35. C4×C16×C89 | C22 | semidirect |
| 55. D1424 | D4 | semidirect |
| 174. #2249 | D89 | semidirect |
| 181. C89 | #33839 | semidirect |
| 186. C2×Q32 | C2×D89 | semidirect |
| 188. C2×SD32 | C2×D89 | semidirect |
| 193. #495 | C2×D89 | semidirect |
| 207. C4×C16 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152035 | 2 |
| #26031936 | 2 |
| #26022362 | 2 |
| #26022304 | 2 |
| #26022191 | 2 |
| #26022162 | 2 |
| C4×D1424 | 2 |
| #26022085 | 2 |
| C89×#2249 | 2 |
| #33839 | 89 |