Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
370 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 370 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. #14271968 | C2 | semidirect |
| 2. #14271601 | C2 | semidirect |
| 3. #14271595 | C2 | semidirect |
| 4. C2×D464 | C2 | semidirect |
| 5. C29×#504 | C2 | semidirect |
| 9. #11745266 | C22 | semidirect |
| 10. C2×D232 | C22 | semidirect |
| 11. C29×M32 | C22 | semidirect |
| 12. C2×C16×C29 | C22 | semidirect |
| 13. Dic232 | C22 | semidirect |
| 14. #11745148 | C22 | semidirect |
| 15. D464 | C22 | semidirect |
| 16. D464 | C22 | semidirect |
| 52. #504 | D29 | semidirect |
| 65. M32 | C2×D29 | semidirect |
| 66. C2×C16 | C2×D29 | semidirect |
| 67. C29 | #3415 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271968 | 2 |
| #14271601 | 2 |
| #14271595 | 2 |
| C2×D464 | 2 |
| C29×#504 | 2 |
| #3415 | 29 |