Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 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×#22583636 | C2 | semidirect |
| 2. C2×#22583630 | C2 | semidirect |
| 3. #31826945 | C2 | semidirect |
| 4. #31826684 | C2 | semidirect |
| 5. #31826677 | C2 | semidirect |
| 6. #31826662 | C2 | semidirect |
| 7. #31826657 | C2 | semidirect |
| 8. #31826492 | C2 | semidirect |
| 9. #31826466 | C2 | semidirect |
| 10. C2×#22583531 | C2 | semidirect |
| 11. #535×C283 | C2 | semidirect |
| 15. C2×#17985382 | C22 | semidirect |
| 17. C2×#17985380 | C22 | semidirect |
| 18. C2×#17985379 | C22 | semidirect |
| 20. C2×#17985377 | C22 | semidirect |
| 23. C4×Dic566 | C22 | semidirect |
| 24. C4×D1132 | C22 | semidirect |
| 29. C4⋊(C283⋊C8) | C22 | semidirect |
| 30. C4⋊(C283⋊C8) | C22 | semidirect |
| 31. #22583534 | C22 | semidirect |
| 34. #22583531 | C22 | semidirect |
| 44. #17985392 | D4 | semidirect |
| 154. C283 | #3045 | semidirect |
| 158. #535 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583636 | 2 |
| C2×#22583630 | 2 |
| #31826945 | 2 |
| #31826684 | 2 |
| #31826677 | 2 |
| #31826662 | 2 |
| #31826657 | 2 |
| #31826492 | 2 |
| #31826466 | 2 |
| C2×#22583531 | 2 |
| #535×C283 | 2 |
| #3045 | 283 |