Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
376 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 376 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. #14271473 | C2 | semidirect |
| 4. #14271462 | C2 | semidirect |
| 5. #14271457 | C2 | semidirect |
| 6. #14271442 | C2 | semidirect |
| 7. C2×#11745155 | C2 | semidirect |
| 8. #14271191 | C2 | semidirect |
| 11. C29×#428 | C2 | semidirect |
| 46. #90805 | Q8 | semidirect |
| 125. #428 | D29 | semidirect |
| 164. C29 | #3083 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271791 | 2 |
| #14271644 | 2 |
| #14271473 | 2 |
| #14271462 | 2 |
| #14271457 | 2 |
| #14271442 | 2 |
| C2×#11745155 | 2 |
| #14271191 | 2 |
| #14271165 | 2 |
| #14271157 | 2 |
| C29×#428 | 2 |
| #3083 | 29 |