Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
256 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 61 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×#11745175 | C2 | semidirect |
| 2. #14271404 | C2 | semidirect |
| 3. #14270964 | C2 | semidirect |
| 4. C22⋊#90768 | C2 | semidirect |
| 12. C2×Dic116 | C22 | semidirect |
| 14. #11745166 | C22 | semidirect |
| 16. C2×#90768 | C22 | semidirect |
| 60. C22×C29 | SD32 | semidirect |
| 88. C29 | #2187 | semidirect |
| 131. C22 | #11745175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745175 | 2 |
| #14271404 | 2 |
| #14270964 | 2 |
| C22⋊#90768 | 2 |
| C22×D8×C29 | 2 |
| #2187 | 29 |