Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
374 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×C4×Dic58 | C2 | semidirect |
| 3. C2×#11745158 | C2 | semidirect |
| 5. #14270925 | C2 | semidirect |
| 6. #14270918 | C2 | semidirect |
| 16. C2×#90783 | C4 | semidirect |
| 82. C2×C4×C29 | SD16 | semidirect |
| 98. Dic58 | C22⋊C4 | semidirect |
| 158. C29 | #1880 | semidirect |
| 225. C2×C4 | #90783 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90783 | 2 |
| C2×C4×Dic58 | 2 |
| C2×#11745158 | 2 |
| C2×#11745180 | 2 |
| #14270925 | 2 |
| #14270918 | 2 |
| C29×#390 | 2 |
| #1880 | 29 |