Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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. #14271526 | C2 | semidirect |
| 4. #14271521 | C2 | semidirect |
| 5. #14271516 | C2 | semidirect |
| 6. #14271508 | C2 | semidirect |
| 7. #14271165 | C2 | semidirect |
| 8. #14271157 | C2 | semidirect |
| 9. C2×#11745180 | C2 | semidirect |
| 10. #14271121 | C2 | semidirect |
| 11. C29×#418 | C2 | semidirect |
| 24. #11745252 | C22 | semidirect |
| 25. #11745250 | C22 | semidirect |
| 33. #11745169 | C22 | semidirect |
| 34. #11745164 | C22 | semidirect |
| 35. #11745163 | C22 | semidirect |
| 36. C8×Dic29 | C22 | semidirect |
| 37. #11745158 | C22 | semidirect |
| 38. #11745158 | C22 | semidirect |
| 39. #11745157 | C22 | semidirect |
| 40. #11745157 | C22 | semidirect |
| 136. #418 | 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 |
| #14271730 | 2 |
| #14271526 | 2 |
| #14271521 | 2 |
| #14271516 | 2 |
| #14271508 | 2 |
| #14271165 | 2 |
| #14271157 | 2 |
| C2×#11745180 | 2 |
| #14271121 | 2 |
| C29×#418 | 2 |
| #3136 | 29 |