Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
652 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 213 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. C2×#11745249 | C2 | semidirect |
| 4. #14271069 | C2 | semidirect |
| 5. #14271051 | C2 | semidirect |
| 6. #14271028 | C2 | semidirect |
| 7. C22⋊C4×Dic29 | C2 | semidirect |
| 8. C42×Dic29 | C2 | semidirect |
| 18. #11745298 | C4 | semidirect |
| 46. C2×Dic58 | C2×C4 | semidirect |
| 51. C22⋊Dic29 | C2×C4 | semidirect |
| 57. C4×Dic29 | C2×C4 | semidirect |
| 106. Dic29 | #124 | semidirect |
| 142. C29 | C4×#124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745298 | 2 |
| C2×#11745249 | 2 |
| C2×D4×Dic29 | 2 |
| #14271069 | 2 |
| #14271051 | 2 |
| #14271028 | 2 |
| C22⋊C4×Dic29 | 2 |
| C42×Dic29 | 2 |
| C29×#390 | 2 |
| C4×#124 | 29 |