Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
556 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 133 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. #31827136 | C2 | semidirect |
| 3. #31826841 | C2 | semidirect |
| 4. #31826716 | C2 | semidirect |
| 5. #31826662 | C2 | semidirect |
| 6. #31826660 | C2 | semidirect |
| 7. #31826608 | C2 | semidirect |
| 8. #31826599 | C2 | semidirect |
| 9. C4×#17985380 | C2 | semidirect |
| 10. #31826543 | C2 | semidirect |
| 11. D42×C283 | C2 | semidirect |
| 12. C2×#17985392 | C22 | semidirect |
| 15. C2×#17985380 | C22 | semidirect |
| 17. C2×#17985377 | C22 | semidirect |
| 18. C2×#17985377 | C22 | semidirect |
| 19. C2×#17985376 | C22 | semidirect |
| 20. #22583607 | C22 | semidirect |
| 22. #22583584 | C22 | semidirect |
| 24. C4×Dic566 | C22 | semidirect |
| 26. #22583541 | C22 | semidirect |
| 27. C4⋊(C283⋊C8) | C22 | semidirect |
| 28. #22583533 | C22 | semidirect |
| 30. #22583531 | C22 | semidirect |
| 31. #22583530 | C22 | semidirect |
| 32. C22⋊(C283⋊C8) | C22 | semidirect |
| 33. C4×C283⋊C8 | C22 | semidirect |
| 52. #17985380 | D4 | semidirect |
| 85. Dic566 | C2×D4 | semidirect |
| 97. C283⋊C8 | C2×D4 | semidirect |
| 138. C4×C283 | AGL(1,ℤ/8) | semidirect |
| 150. C283 | #3274 | semidirect |
| 154. D42 | D283 | semidirect |
| 291. C4 | #22583636 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583636 | 2 |
| #31827136 | 2 |
| #31826841 | 2 |
| #31826716 | 2 |
| #31826662 | 2 |
| #31826660 | 2 |
| #31826608 | 2 |
| #31826599 | 2 |
| C4×#17985380 | 2 |
| #31826543 | 2 |
| D42×C283 | 2 |
| #3274 | 283 |