Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×Dic116 | C2 | semidirect |
| 3. C22×#90773 | C2 | semidirect |
| 4. C2×#11745286 | C2 | semidirect |
| 5. #14271327 | C2 | direct (N × H) |
| 6. C2×#11745164 | C2 | semidirect |
| 7. C2×#11745169 | C2 | semidirect |
| 8. C2×C29×C22⋊C8 | C2 | semidirect |
| 24. #11745286 | C22 | semidirect |
| 27. C2×Dic116 | C22 | semidirect |
| 29. C2×#90773 | C22 | semidirect |
| 30. C29×C22⋊C8 | C22 | semidirect |
| 31. #11745169 | C22 | semidirect |
| 32. #11745164 | C22 | semidirect |
| 137. C2×C22⋊C8 | D29 | semidirect |
| 139. C2×C29 | #452 | semidirect |
| 167. C22⋊C8 | C2×D29 | semidirect |
| 168. C29 | C2×#452 | semidirect |
| 267. C2 | #14271327 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90805 | 2 |
| C22×Dic116 | 2 |
| C22×#90773 | 2 |
| C2×#11745286 | 2 |
| #14271327 | 2 |
| C2×#11745164 | 2 |
| C2×#11745169 | 2 |
| C2×C29×C22⋊C8 | 2 |
| C2×#452 | 29 |