Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
372 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 133 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. #14271791 | C2 | semidirect |
| 3. #14271532 | C2 | semidirect |
| 4. #14271523 | C2 | semidirect |
| 5. #14271518 | C2 | semidirect |
| 6. #14271514 | C2 | semidirect |
| 7. #14271173 | C2 | semidirect |
| 10. C2×#11745164 | C2 | semidirect |
| 11. C29×#405 | C2 | semidirect |
| 133. #405 | D29 | semidirect |
| 168. C29 | #3137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271791 | 2 |
| #14271739 | 2 |
| #14271532 | 2 |
| #14271523 | 2 |
| #14271518 | 2 |
| #14271514 | 2 |
| #14271173 | 2 |
| #14271165 | 2 |
| #14271160 | 2 |
| C2×#11745164 | 2 |
| C29×#405 | 2 |
| #3137 | 29 |