Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 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. #31827119 | C2 | semidirect |
| 2. #31826811 | C2 | semidirect |
| 3. #31826776 | C2 | semidirect |
| 4. #31826745 | C2 | semidirect |
| 5. #31826699 | C2 | semidirect |
| 6. #31826657 | C2 | semidirect |
| 7. #31826599 | C2 | semidirect |
| 8. C4×#17985377 | C2 | semidirect |
| 9. D4×C283⋊C8 | C2 | semidirect |
| 10. C2×#22583531 | C2 | semidirect |
| 11. D42×C283 | C2 | semidirect |
| 14. C2×#17985377 | C22 | semidirect |
| 15. C22×C283⋊C8 | C22 | semidirect |
| 16. #22583610 | C22 | semidirect |
| 19. #22583584 | C22 | semidirect |
| 20. C4×D1132 | C22 | semidirect |
| 21. C2×C4⋊Dic283 | C22 | semidirect |
| 22. #22583543 | C22 | semidirect |
| 23. #22583543 | C22 | semidirect |
| 24. C4⋊(C283⋊C8) | C22 | semidirect |
| 27. #22583531 | C22 | semidirect |
| 28. #22583531 | C22 | semidirect |
| 29. #22583531 | C22 | semidirect |
| 30. #22583530 | C22 | semidirect |
| 31. C22⋊(C283⋊C8) | C22 | semidirect |
| 32. C4×C283⋊C8 | C22 | semidirect |
| 103. D4×C283 | D8 | semidirect |
| 104. D4×C283 | #41 | semidirect |
| 142. C283 | #3294 | semidirect |
| 145. D42 | D283 | semidirect |
| 239. D4 | #17985377 | semidirect |
| 240. D4 | #17985391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827119 | 2 |
| #31826811 | 2 |
| #31826776 | 2 |
| #31826745 | 2 |
| #31826699 | 2 |
| #31826657 | 2 |
| #31826599 | 2 |
| C4×#17985377 | 2 |
| D4×C283⋊C8 | 2 |
| C2×#22583531 | 2 |
| D42×C283 | 2 |
| #3294 | 283 |