Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 360 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. #14271980 | C2 | semidirect |
| 2. #14271968 | C2 | semidirect |
| 3. #14271606 | C2 | semidirect |
| 4. #14271601 | C2 | semidirect |
| 5. #14271595 | C2 | semidirect |
| 6. C2×#11745148 | C2 | semidirect |
| 7. C29×#504 | C2 | semidirect |
| 13. C2×Dic116 | C22 | semidirect |
| 15. #11745266 | C22 | semidirect |
| 17. C29×M32 | C22 | semidirect |
| 18. C2×C16×C29 | C22 | semidirect |
| 19. Dic232 | C22 | semidirect |
| 20. #11745148 | C22 | semidirect |
| 21. #11745148 | C22 | semidirect |
| 22. #11745148 | C22 | semidirect |
| 23. D464 | C22 | semidirect |
| 77. #504 | D29 | semidirect |
| 96. M32 | C2×D29 | semidirect |
| 97. C2×C16 | C2×D29 | semidirect |
| 98. C29 | #3416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271980 | 2 |
| #14271968 | 2 |
| #14271606 | 2 |
| #14271601 | 2 |
| #14271595 | 2 |
| C2×#11745148 | 2 |
| C29×#504 | 2 |
| #3416 | 29 |