Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
282 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 1. #14271791 | C2 | semidirect |
| 5. #14270931 | C2 | semidirect |
| 6. #14270923 | C2 | semidirect |
| 7. C29×#339 | C2 | semidirect |
| 34. C2×D116 | Q8 | semidirect |
| 113. #339 | D29 | semidirect |
| 137. C29 | #2027 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271791 | 2 |
| #14271169 | 2 |
| #14271167 | 2 |
| #14271065 | 2 |
| #14270931 | 2 |
| #14270923 | 2 |
| C29×#339 | 2 |
| #2027 | 29 |