Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
462 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 462 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. #31827172 | C2 | semidirect |
| 2. #31826811 | C2 | semidirect |
| 3. #31826781 | C2 | semidirect |
| 4. #31826755 | C2 | semidirect |
| 5. #31826692 | C2 | semidirect |
| 6. #31826662 | C2 | semidirect |
| 7. #31826616 | C2 | semidirect |
| 8. C4×#17985380 | C2 | semidirect |
| 9. D4×C283⋊C8 | C2 | semidirect |
| 10. C2×#22583531 | C2 | semidirect |
| 13. C2×#17985380 | C22 | semidirect |
| 14. C22×C283⋊C8 | C22 | semidirect |
| 15. #22583610 | C22 | semidirect |
| 17. #22583589 | C22 | semidirect |
| 19. C4×Dic566 | C22 | semidirect |
| 21. C2×C4⋊Dic283 | C22 | semidirect |
| 22. #22583541 | C22 | semidirect |
| 23. #22583541 | C22 | semidirect |
| 24. C4⋊(C283⋊C8) | C22 | semidirect |
| 25. #22583533 | C22 | semidirect |
| 28. #22583531 | C22 | semidirect |
| 29. #22583531 | C22 | semidirect |
| 30. #22583531 | C22 | semidirect |
| 31. C22⋊(C283⋊C8) | C22 | semidirect |
| 32. C4×C283⋊C8 | C22 | semidirect |
| 100. D4×C283 | SD16 | semidirect |
| 136. C283 | #3295 | semidirect |
| 230. D4 | #17985380 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827172 | 2 |
| #31826811 | 2 |
| #31826781 | 2 |
| #31826755 | 2 |
| #31826692 | 2 |
| #31826662 | 2 |
| #31826616 | 2 |
| C4×#17985380 | 2 |
| D4×C283⋊C8 | 2 |
| C2×#22583531 | 2 |
| D42×C283 | 2 |
| #3295 | 283 |