Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
752 conjugacy classes of subgroups; only the 341 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 341 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 |
|---|---|---|
| 3. #14271014 | C2 | semidirect |
| 5. #14271009 | C2 | semidirect |
| 6. C42×Dic29 | C2 | semidirect |
| 7. C29×#376 | C2 | semidirect |
| 18. #11745234 | C4 | semidirect |
| 19. C42×D29 | C4 | semidirect |
| 34. C42×C29 | C2×C4 | semidirect |
| 36. #90779 | C2×C4 | semidirect |
| 40. C4×Dic29 | C2×C4 | semidirect |
| 58. C4×D29 | C42 | semidirect |
| 71. Dic29 | #117 | semidirect |
| 77. #376 | D29 | semidirect |
| 97. C29 | C4×#117 | semidirect |
| 116. C42 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745234 | 2 |
| C2×C42×D29 | 2 |
| #14271014 | 2 |
| #14271010 | 2 |
| #14271009 | 2 |
| C42×Dic29 | 2 |
| C29×#376 | 2 |
| C4×#117 | 29 |