Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 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 |
|---|---|---|
| 1. #14271899 | C2 | semidirect |
| 2. #14271870 | C2 | semidirect |
| 3. #14271516 | C2 | semidirect |
| 4. #14271509 | C2 | semidirect |
| 5. #14271461 | C2 | semidirect |
| 6. #14271459 | C2 | semidirect |
| 7. #14271376 | C2 | semidirect |
| 8. #14271287 | C2 | semidirect |
| 9. C4×#90783 | C2 | semidirect |
| 10. D8×Dic29 | C2 | semidirect |
| 163. C29 | #3361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271899 | 2 |
| #14271870 | 2 |
| #14271516 | 2 |
| #14271509 | 2 |
| #14271461 | 2 |
| #14271459 | 2 |
| #14271376 | 2 |
| #14271287 | 2 |
| C4×#90783 | 2 |
| D8×Dic29 | 2 |
| C29×#459 | 2 |
| #3361 | 29 |