Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
230 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 53 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. C2×#11745266 | C2 | semidirect |
| 2. C2×#11745175 | C2 | semidirect |
| 3. C2×#11745174 | C2 | semidirect |
| 4. #14270966 | C2 | semidirect |
| 5. #14270963 | C2 | semidirect |
| 6. C22⋊#90768 | C2 | semidirect |
| 7. C29×#466 | C2 | semidirect |
| 41. Dic116 | D4 | semidirect |
| 43. D232 | D4 | semidirect |
| 87. #466 | D29 | semidirect |
| 112. C29 | #2186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745266 | 2 |
| C2×#11745175 | 2 |
| C2×#11745174 | 2 |
| #14270966 | 2 |
| #14270963 | 2 |
| C22⋊#90768 | 2 |
| C29×#466 | 2 |
| #2186 | 29 |