Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
656 conjugacy classes of subgroups; only the 317 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 317 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. #14271062 | C2 | semidirect |
| 5. C4×C4⋊Dic29 | C2 | semidirect |
| 9. C29×#117 | C4 | semidirect |
| 33. C4⋊C4×C29 | C2×C4 | semidirect |
| 35. C42×C29 | C2×C4 | semidirect |
| 48. C2×C4×C29 | C4⋊C4 | semidirect |
| 90. #117 | Dic29 | semidirect |
| 102. C29 | #2296 | semidirect |
| 116. C4⋊C4 | C2×Dic29 | semidirect |
| 122. C42 | C2×Dic29 | semidirect |
| 135. C2×C4 | C4⋊Dic29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745288 | 2 |
| C22×C4×Dic29 | 2 |
| #14271062 | 2 |
| #14271038 | 2 |
| C4×C4⋊Dic29 | 2 |
| C2×C29×#117 | 2 |
| #2296 | 29 |