Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
256 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 256 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 |
|---|---|---|
| 2. C2×#11745148 | C2 | semidirect |
| 3. C2×#11745175 | C2 | semidirect |
| 4. #14271405 | C2 | semidirect |
| 5. #14270963 | C2 | semidirect |
| 6. #14270942 | C2 | semidirect |
| 7. C29×#357 | C2 | semidirect |
| 13. C2×Dic116 | C22 | semidirect |
| 17. C2×C16×C29 | C22 | semidirect |
| 18. C29×#107 | C22 | semidirect |
| 20. C2×#90768 | C22 | semidirect |
| 80. C2×D29 | SD32 | semidirect |
| 91. #357 | D29 | semidirect |
| 111. C2×C16 | C2×D29 | semidirect |
| 112. #107 | C2×D29 | semidirect |
| 114. C29 | #2187 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D29 | 2 |
| C2×#11745148 | 2 |
| C2×#11745175 | 2 |
| #14271405 | 2 |
| #14270963 | 2 |
| #14270942 | 2 |
| C29×#357 | 2 |
| #2187 | 29 |