Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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×#22583629 | C2 | semidirect |
| 2. C2×D8×D283 | C2 | semidirect |
| 3. #31826899 | C2 | direct (N × H) |
| 4. C2×#22583555 | C2 | semidirect |
| 5. C2×#22583554 | C2 | semidirect |
| 6. C2×#22583551 | C2 | semidirect |
| 7. C2×#22583549 | C2 | semidirect |
| 8. C2×D16×C283 | C2 | semidirect |
| 12. #22583629 | C22 | semidirect |
| 13. C2×Dic1132 | C22 | semidirect |
| 18. D8×D283 | C22 | semidirect |
| 20. #22583555 | C22 | semidirect |
| 21. #22583554 | C22 | semidirect |
| 22. #22583551 | C22 | semidirect |
| 23. #22583549 | C22 | semidirect |
| 24. C2×C283⋊C16 | C22 | semidirect |
| 26. C2×D8×C283 | C22 | semidirect |
| 27. D16×C283 | C22 | semidirect |
| 28. C2×C16×C283 | C22 | semidirect |
| 41. Dic1132 | C23 | semidirect |
| 49. C283⋊C16 | C23 | semidirect |
| 55. D8×C283 | C23 | semidirect |
| 57. C16×C283 | C23 | semidirect |
| 99. C2×C283 | #509 | semidirect |
| 103. C283 | C2×#509 | semidirect |
| 111. C2×D16 | D283 | semidirect |
| 124. C2×D8 | C2×D283 | semidirect |
| 129. D16 | C2×D283 | semidirect |
| 132. C2×C16 | C2×D283 | semidirect |
| 155. D8 | C22×D283 | semidirect |
| 161. C16 | C22×D283 | semidirect |
| 205. C2 | #31826899 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583629 | 2 |
| C2×D8×D283 | 2 |
| #31826899 | 2 |
| C2×#22583555 | 2 |
| C2×#22583554 | 2 |
| C2×#22583551 | 2 |
| C2×#22583549 | 2 |
| C2×D16×C283 | 2 |
| C2×#509 | 283 |