Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 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. #14271791 | C2 | semidirect |
| 3. #14271528 | C2 | semidirect |
| 4. #14271523 | C2 | semidirect |
| 5. #14271518 | C2 | semidirect |
| 6. #14271510 | C2 | semidirect |
| 7. #14271169 | C2 | semidirect |
| 8. #14271165 | C2 | semidirect |
| 9. #14271160 | C2 | semidirect |
| 10. C2×#11745169 | C2 | semidirect |
| 11. C29×#405 | C2 | semidirect |
| 27. #11745232 | C22 | semidirect |
| 28. #11745231 | C22 | semidirect |
| 29. C29×#97 | C22 | semidirect |
| 30. C4×C8×C29 | C22 | semidirect |
| 35. #11745169 | C22 | semidirect |
| 36. #11745169 | C22 | semidirect |
| 37. #11745169 | C22 | semidirect |
| 38. #11745164 | C22 | semidirect |
| 39. #11745164 | C22 | semidirect |
| 40. #11745164 | C22 | semidirect |
| 140. #405 | D29 | semidirect |
| 174. #97 | C2×D29 | semidirect |
| 175. C4×C8 | C2×D29 | semidirect |
| 176. C29 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271791 | 2 |
| #14271732 | 2 |
| #14271528 | 2 |
| #14271523 | 2 |
| #14271518 | 2 |
| #14271510 | 2 |
| #14271169 | 2 |
| #14271165 | 2 |
| #14271160 | 2 |
| C2×#11745169 | 2 |
| C29×#405 | 2 |
| #3136 | 29 |