Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 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. C2×#11745294 | C2 | semidirect |
| 2. C2×#11745312 | C2 | semidirect |
| 3. #14271643 | C2 | semidirect |
| 4. #14271382 | C2 | semidirect |
| 5. #14271375 | C2 | semidirect |
| 6. #14271360 | C2 | semidirect |
| 7. #14271355 | C2 | semidirect |
| 8. #14271190 | C2 | semidirect |
| 9. #14271164 | C2 | semidirect |
| 10. C2×#11745180 | C2 | semidirect |
| 11. C29×#535 | C2 | semidirect |
| 22. C2×#90785 | C22 | semidirect |
| 23. C2×#90784 | C22 | semidirect |
| 25. C2×#90783 | C22 | semidirect |
| 28. C2×#90782 | C22 | semidirect |
| 35. C4×D116 | C22 | semidirect |
| 36. C4×Dic58 | C22 | semidirect |
| 37. #11745183 | C22 | semidirect |
| 40. #11745180 | C22 | semidirect |
| 41. C4⋊#6597 | C22 | semidirect |
| 42. C4⋊#6597 | C22 | semidirect |
| 60. #90805 | D4 | semidirect |
| 150. #535 | D29 | semidirect |
| 197. C29 | #3045 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745294 | 2 |
| C2×#11745312 | 2 |
| #14271643 | 2 |
| #14271382 | 2 |
| #14271375 | 2 |
| #14271360 | 2 |
| #14271355 | 2 |
| #14271190 | 2 |
| #14271164 | 2 |
| C2×#11745180 | 2 |
| C29×#535 | 2 |
| #3045 | 29 |