Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 2. #14271641 | C2 | semidirect |
| 4. #14271266 | C2 | semidirect |
| 5. #14271248 | C2 | semidirect |
| 6. #14271199 | C2 | semidirect |
| 8. #14271121 | C2 | semidirect |
| 9. C29×#419 | C2 | semidirect |
| 15. Q8×Dic29 | C22 | semidirect |
| 16. C2×#90784 | C4 | semidirect |
| 26. C29×#103 | C22 | semidirect |
| 28. #11745163 | C22 | semidirect |
| 29. C8×Dic29 | C22 | semidirect |
| 30. #11745156 | C22 | semidirect |
| 31. #11745155 | C22 | semidirect |
| 35. C2×Q8×C29 | C2×C4 | semidirect |
| 51. #90784 | C2×C4 | semidirect |
| 52. #90784 | C2×C4 | semidirect |
| 60. C2×#6597 | C2×C4 | semidirect |
| 106. #419 | D29 | semidirect |
| 131. #103 | C2×D29 | semidirect |
| 135. C29 | #2949 | semidirect |
| 139. C2×Q8 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90784 | 2 |
| #14271641 | 2 |
| #14271637 | 2 |
| #14271266 | 2 |
| #14271248 | 2 |
| #14271199 | 2 |
| #14271169 | 2 |
| #14271121 | 2 |
| C29×#419 | 2 |
| #2949 | 29 |