Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
390 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 390 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 |
|---|---|---|
| 1. C22×#90785 | C2 | semidirect |
| 4. C2×#11745158 | C2 | semidirect |
| 6. #14270918 | C2 | semidirect |
| 7. C29×#391 | C2 | semidirect |
| 125. #391 | D29 | semidirect |
| 152. C29 | #2015 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90785 | 2 |
| C22×#90784 | 2 |
| C2×#11745237 | 2 |
| C2×#11745158 | 2 |
| C2×#11745157 | 2 |
| #14270918 | 2 |
| C29×#391 | 2 |
| #2015 | 29 |