Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
430 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 115 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. #14271714 | C2 | semidirect |
| 2. #14271710 | C2 | semidirect |
| 3. #14271452 | C2 | semidirect |
| 4. #14271450 | C2 | semidirect |
| 5. #14271417 | C2 | semidirect |
| 6. #14271415 | C2 | semidirect |
| 7. #14271359 | C2 | semidirect |
| 8. #14271358 | C2 | semidirect |
| 9. #14271357 | C2 | semidirect |
| 10. #14271185 | C2 | semidirect |
| 11. C29×#476 | C2 | semidirect |
| 148. #476 | D29 | semidirect |
| 193. C29 | #3253 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271714 | 2 |
| #14271710 | 2 |
| #14271452 | 2 |
| #14271450 | 2 |
| #14271417 | 2 |
| #14271415 | 2 |
| #14271359 | 2 |
| #14271358 | 2 |
| #14271357 | 2 |
| #14271185 | 2 |
| C29×#476 | 2 |
| #3253 | 29 |