Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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. #125×D29 | C2 | semidirect |
| 3. #14271530 | C2 | semidirect |
| 4. #14271526 | C2 | semidirect |
| 5. #14271520 | C2 | semidirect |
| 6. #14271518 | C2 | semidirect |
| 7. #14271517 | C2 | semidirect |
| 8. #14271163 | C2 | semidirect |
| 9. #14271161 | C2 | semidirect |
| 10. C4×#90772 | C2 | semidirect |
| 11. C29×#488 | C2 | semidirect |
| 117. #488 | D29 | semidirect |
| 153. C29 | #3142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271712 | 2 |
| #125×D29 | 2 |
| #14271530 | 2 |
| #14271526 | 2 |
| #14271520 | 2 |
| #14271518 | 2 |
| #14271517 | 2 |
| #14271163 | 2 |
| #14271161 | 2 |
| C4×#90772 | 2 |
| C29×#488 | 2 |
| #3142 | 29 |