Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
448 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 127 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. #31827020 | C2 | semidirect |
| 3. #31826797 | C2 | semidirect |
| 4. #31826752 | C2 | semidirect |
| 5. #31826671 | C2 | semidirect |
| 6. #31826670 | C2 | semidirect |
| 8. #31826556 | C2 | semidirect |
| 9. #31826552 | C2 | semidirect |
| 10. #31826517 | C2 | semidirect |
| 11. #476×C283 | C2 | semidirect |
| 16. #22583610 | C22 | semidirect |
| 21. #22583575 | C22 | semidirect |
| 31. #22583541 | C22 | semidirect |
| 32. C4⋊(C283⋊C8) | C22 | semidirect |
| 33. #22583535 | C22 | semidirect |
| 34. #22583533 | C22 | semidirect |
| 37. C8×Dic283 | C22 | semidirect |
| 38. C4⋊Q8×C283 | C22 | semidirect |
| 40. #106×C283 | C22 | semidirect |
| 41. C4⋊C8×C283 | C22 | semidirect |
| 105. C4×D283 | SD16 | semidirect |
| 146. C283 | #3101 | semidirect |
| 152. #476 | D283 | semidirect |
| 164. C4⋊Q8 | C2×D283 | semidirect |
| 181. #106 | C2×D283 | semidirect |
| 183. C4⋊C8 | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827020 | 2 |
| C4×D4×D283 | 2 |
| #31826797 | 2 |
| #31826752 | 2 |
| #31826671 | 2 |
| #31826670 | 2 |
| #31826617 | 2 |
| #31826556 | 2 |
| #31826552 | 2 |
| #31826517 | 2 |
| #476×C283 | 2 |
| #3101 | 283 |