Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
286 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 83 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. #14271203 | C2 | semidirect |
| 5. #14270932 | C2 | semidirect |
| 6. #14270923 | C2 | semidirect |
| 7. C29×#382 | C2 | semidirect |
| 25. #11745153 | C4 | semidirect |
| 44. C42×C29 | C2×C4 | semidirect |
| 55. #90777 | C2×C4 | semidirect |
| 110. #382 | D29 | semidirect |
| 137. C29 | #1860 | semidirect |
| 169. C42 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271644 | 2 |
| #14271203 | 2 |
| C2×#11745153 | 2 |
| #14271162 | 2 |
| #14270932 | 2 |
| #14270923 | 2 |
| C29×#382 | 2 |
| #1860 | 29 |