Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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×#22583638 | C2 | semidirect |
| 2. C22×D2264 | C2 | semidirect |
| 3. #31827034 | C2 | semidirect |
| 4. #31826939 | C2 | semidirect |
| 5. #31826681 | C2 | semidirect |
| 6. #31826661 | C2 | semidirect |
| 7. #31826471 | C2 | semidirect |
| 8. #31826462 | C2 | semidirect |
| 9. #424×C283 | C2 | semidirect |
| 14. C2×#17985381 | C22 | semidirect |
| 17. C2×D2264 | C22 | semidirect |
| 18. #22583607 | C22 | semidirect |
| 19. #22583598 | C22 | semidirect |
| 22. C4×D1132 | C22 | semidirect |
| 26. #22583535 | C22 | semidirect |
| 27. #22583532 | C22 | semidirect |
| 28. #22583532 | C22 | semidirect |
| 32. C4⋊C8×C283 | C22 | semidirect |
| 44. C2×D1132 | D4 | semidirect |
| 121. C283 | #3041 | semidirect |
| 129. #424 | D283 | semidirect |
| 151. C4⋊C8 | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583638 | 2 |
| C22×D2264 | 2 |
| #31827034 | 2 |
| #31826939 | 2 |
| #31826681 | 2 |
| #31826661 | 2 |
| #31826471 | 2 |
| #31826462 | 2 |
| #424×C283 | 2 |
| #3041 | 283 |