Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
652 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 209 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. #14271068 | C2 | semidirect |
| 6. #14271052 | C2 | semidirect |
| 7. #14271010 | C2 | semidirect |
| 8. C42×Dic29 | C2 | semidirect |
| 9. C29×#382 | C2 | semidirect |
| 27. #11745237 | C4 | semidirect |
| 46. C2×Dic58 | C2×C4 | semidirect |
| 49. C42×C29 | C2×C4 | semidirect |
| 52. #90781 | C2×C4 | semidirect |
| 106. Dic29 | #124 | semidirect |
| 113. #382 | D29 | semidirect |
| 142. C29 | C4×#124 | semidirect |
| 171. C42 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745237 | 2 |
| C2×#11745249 | 2 |
| C2×#11745255 | 2 |
| #14271068 | 2 |
| #14271064 | 2 |
| #14271052 | 2 |
| #14271010 | 2 |
| C42×Dic29 | 2 |
| C29×#382 | 2 |
| C4×#124 | 29 |