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. #14271713 | C2 | semidirect |
| 2. C4×#90805 | C2 | semidirect |
| 3. #14271488 | C2 | semidirect |
| 4. #14271449 | C2 | semidirect |
| 5. #14271444 | C2 | semidirect |
| 6. #14271364 | C2 | semidirect |
| 7. #14271359 | C2 | semidirect |
| 8. #14271310 | C2 | semidirect |
| 9. #14271276 | C2 | semidirect |
| 10. #14271265 | C2 | semidirect |
| 11. C29×#432 | C2 | semidirect |
| 107. D116 | #41 | semidirect |
| 114. Dic58 | #41 | semidirect |
| 149. #432 | 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 |
|---|---|
| #14271713 | 2 |
| C4×#90805 | 2 |
| #14271488 | 2 |
| #14271449 | 2 |
| #14271444 | 2 |
| #14271364 | 2 |
| #14271359 | 2 |
| #14271310 | 2 |
| #14271276 | 2 |
| #14271265 | 2 |
| C29×#432 | 2 |
| #3115 | 29 |