Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
304 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 89 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. #14271173 | C2 | semidirect |
| 4. C2×#11745172 | C2 | semidirect |
| 5. #14270935 | C2 | semidirect |
| 6. #14270921 | C2 | semidirect |
| 17. C2×#90785 | C4 | semidirect |
| 18. C2×#90783 | C4 | semidirect |
| 132. C29 | #1902 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745313 | 2 |
| #14271180 | 2 |
| #14271173 | 2 |
| C2×#11745172 | 2 |
| #14270935 | 2 |
| #14270921 | 2 |
| C29×#568 | 2 |
| #1902 | 29 |