Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
400 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 129 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. #14271716 | C2 | semidirect |
| 3. #14271519 | C2 | semidirect |
| 4. #14271516 | C2 | semidirect |
| 5. #14271512 | C2 | semidirect |
| 6. #14271508 | C2 | semidirect |
| 7. #14271160 | C2 | semidirect |
| 8. #14271159 | C2 | semidirect |
| 9. #14271157 | C2 | semidirect |
| 10. C2×C8×Dic29 | C2 | semidirect |
| 11. C29×#416 | C2 | semidirect |
| 130. #416 | D29 | semidirect |
| 164. C29 | #3131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271716 | 2 |
| #14271709 | 2 |
| #14271519 | 2 |
| #14271516 | 2 |
| #14271512 | 2 |
| #14271508 | 2 |
| #14271160 | 2 |
| #14271159 | 2 |
| #14271157 | 2 |
| C2×C8×Dic29 | 2 |
| C29×#416 | 2 |
| #3131 | 29 |