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. #14271794 | C2 | semidirect |
| 3. #14271526 | C2 | semidirect |
| 4. #14271524 | C2 | semidirect |
| 5. #14271519 | C2 | semidirect |
| 6. #14271508 | C2 | semidirect |
| 7. #14271169 | C2 | semidirect |
| 8. #14271159 | C2 | semidirect |
| 9. C2×#11745157 | C2 | semidirect |
| 10. #14271121 | C2 | semidirect |
| 11. C29×#417 | C2 | semidirect |
| 26. #11745252 | C22 | semidirect |
| 28. #11745250 | C22 | semidirect |
| 29. C29×#103 | C22 | semidirect |
| 30. C29×#102 | C22 | semidirect |
| 31. #11745183 | C22 | semidirect |
| 32. #11745183 | C22 | semidirect |
| 33. #11745180 | C22 | semidirect |
| 34. #11745180 | C22 | semidirect |
| 37. #11745163 | C22 | semidirect |
| 38. C8×Dic29 | C22 | semidirect |
| 137. #417 | D29 | semidirect |
| 166. #103 | C2×D29 | semidirect |
| 173. #102 | 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 |
|---|---|
| #14271794 | 2 |
| #14271727 | 2 |
| #14271526 | 2 |
| #14271524 | 2 |
| #14271519 | 2 |
| #14271508 | 2 |
| #14271169 | 2 |
| #14271159 | 2 |
| C2×#11745157 | 2 |
| #14271121 | 2 |
| C29×#417 | 2 |
| #3136 | 29 |