Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
502 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 131 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×#15689552 | C2 | semidirect |
| 2. C2×D16×D47 | C2 | semidirect |
| 3. #20245699 | C2 | direct (N × H) |
| 4. C2×#15688962 | C2 | semidirect |
| 5. C2×#15688961 | C2 | semidirect |
| 6. C2×#15688958 | C2 | semidirect |
| 7. C2×#15688956 | C2 | semidirect |
| 8. C2×C47×D32 | C2 | semidirect |
| 12. #15689552 | C22 | semidirect |
| 13. C2×Dic376 | C22 | semidirect |
| 18. D16×D47 | C22 | semidirect |
| 20. #15688962 | C22 | semidirect |
| 21. #15688961 | C22 | semidirect |
| 22. #15688958 | C22 | semidirect |
| 23. #15688956 | C22 | semidirect |
| 24. C2×C47⋊C32 | C22 | semidirect |
| 26. C2×D16×C47 | C22 | semidirect |
| 27. C47×D32 | C22 | semidirect |
| 28. C2×C32×C47 | C22 | semidirect |
| 41. Dic376 | C23 | semidirect |
| 49. C47⋊C32 | C23 | semidirect |
| 55. D16×C47 | C23 | semidirect |
| 57. C32×C47 | C23 | semidirect |
| 134. C2×D32 | D47 | semidirect |
| 138. C2×C47 | #2263 | semidirect |
| 153. C2×D16 | C2×D47 | semidirect |
| 158. D32 | C2×D47 | semidirect |
| 161. C2×C32 | C2×D47 | semidirect |
| 162. C47 | C2×#2263 | semidirect |
| 185. D16 | C22×D47 | semidirect |
| 191. C32 | C22×D47 | semidirect |
| 265. C2 | #20245699 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689552 | 2 |
| C2×D16×D47 | 2 |
| #20245699 | 2 |
| C2×#15688962 | 2 |
| C2×#15688961 | 2 |
| C2×#15688958 | 2 |
| C2×#15688956 | 2 |
| C2×C47×D32 | 2 |
| C2×#2263 | 47 |