Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
312 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 312 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 |
|---|---|---|
| 4. C2×#11745164 | C2 | semidirect |
| 5. C2×#11745172 | C2 | semidirect |
| 6. #14270931 | C2 | semidirect |
| 7. C29×#341 | C2 | semidirect |
| 16. #11745271 | C4 | semidirect |
| 117. #341 | D29 | semidirect |
| 144. C29 | #1908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745271 | 2 |
| C2×#11745263 | 2 |
| #14271165 | 2 |
| C2×#11745164 | 2 |
| C2×#11745172 | 2 |
| #14270931 | 2 |
| C29×#341 | 2 |
| #1908 | 29 |