Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 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. #14271717 | C2 | semidirect |
| 3. #14271459 | C2 | semidirect |
| 4. #14271458 | C2 | semidirect |
| 5. #14271441 | C2 | semidirect |
| 6. #14271408 | C2 | semidirect |
| 7. #14271406 | C2 | semidirect |
| 8. #14271366 | C2 | semidirect |
| 9. #14271360 | C2 | semidirect |
| 10. #14271185 | C2 | semidirect |
| 11. C29×#460 | C2 | semidirect |
| 142. #460 | D29 | semidirect |
| 180. C29 | #3254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271717 | 2 |
| #14271711 | 2 |
| #14271459 | 2 |
| #14271458 | 2 |
| #14271441 | 2 |
| #14271408 | 2 |
| #14271406 | 2 |
| #14271366 | 2 |
| #14271360 | 2 |
| #14271185 | 2 |
| C29×#460 | 2 |
| #3254 | 29 |