Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 430 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. C4×#90805 | C2 | semidirect |
| 2. #14271484 | C2 | semidirect |
| 3. #14271445 | C2 | semidirect |
| 4. #14271440 | C2 | semidirect |
| 5. #14271360 | C2 | semidirect |
| 6. #14271355 | C2 | semidirect |
| 7. #14271306 | C2 | semidirect |
| 8. #14271273 | C2 | semidirect |
| 9. #14271263 | C2 | semidirect |
| 10. #14271220 | C2 | semidirect |
| 11. C29×#532 | C2 | semidirect |
| 109. D116 | #41 | semidirect |
| 114. Dic58 | #41 | semidirect |
| 139. #532 | D29 | semidirect |
| 187. C29 | #3115 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#90805 | 2 |
| #14271484 | 2 |
| #14271445 | 2 |
| #14271440 | 2 |
| #14271360 | 2 |
| #14271355 | 2 |
| #14271306 | 2 |
| #14271273 | 2 |
| #14271263 | 2 |
| #14271220 | 2 |
| C29×#532 | 2 |
| #3115 | 29 |