Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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. #14271720 | C2 | semidirect |
| 3. #14271505 | C2 | semidirect |
| 4. #14271459 | C2 | semidirect |
| 5. #14271454 | C2 | semidirect |
| 6. #14271374 | C2 | semidirect |
| 7. #14271369 | C2 | semidirect |
| 9. #14271271 | C2 | semidirect |
| 10. #14271265 | C2 | semidirect |
| 11. C29×#432 | C2 | semidirect |
| 142. #432 | D29 | semidirect |
| 179. C29 | #3116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271720 | 2 |
| C4×#90805 | 2 |
| #14271505 | 2 |
| #14271459 | 2 |
| #14271454 | 2 |
| #14271374 | 2 |
| #14271369 | 2 |
| #14271327 | 2 |
| #14271271 | 2 |
| #14271265 | 2 |
| C29×#432 | 2 |
| #3116 | 29 |