Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
360 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 360 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 |
|---|---|---|
| 3. #14271172 | C2 | semidirect |
| 5. #14270924 | C2 | semidirect |
| 6. #14270922 | C2 | semidirect |
| 7. C29×#419 | C2 | semidirect |
| 13. #11745309 | C4 | semidirect |
| 30. C2×Q8×C29 | C2×C4 | semidirect |
| 53. C4×Dic29 | C2×C4 | semidirect |
| 106. #419 | D29 | semidirect |
| 131. C29 | #1885 | semidirect |
| 138. C2×Q8 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745309 | 2 |
| #14271637 | 2 |
| #14271172 | 2 |
| C2×#11745171 | 2 |
| #14270924 | 2 |
| #14270922 | 2 |
| C29×#419 | 2 |
| #1885 | 29 |