Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
738 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 249 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 |
|---|---|---|
| 2. #41×Dic29 | C2 | semidirect |
| 3. #14271179 | C2 | semidirect |
| 4. C2×#11745173 | C2 | semidirect |
| 5. C29×#568 | C2 | semidirect |
| 7. #11745365 | C4 | semidirect |
| 8. #11745364 | C4 | semidirect |
| 14. C2×M16×C29 | C22 | semidirect |
| 17. #11745288 | C22 | semidirect |
| 18. C2×C4×Dic29 | C22 | semidirect |
| 19. #11745173 | C22 | semidirect |
| 20. #11745173 | C22 | semidirect |
| 34. #90805 | C2×C4 | semidirect |
| 36. C2×D116 | C2×C4 | semidirect |
| 38. C2×Dic58 | C2×C4 | semidirect |
| 81. #568 | D29 | semidirect |
| 97. C2×M16 | C2×D29 | semidirect |
| 104. C29 | #2901 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271999 | 2 |
| #41×Dic29 | 2 |
| #14271179 | 2 |
| C2×#11745173 | 2 |
| C29×#568 | 2 |
| #2901 | 29 |