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×#90785 | C2 | semidirect |
| 3. C22×#90784 | C2 | semidirect |
| 4. #14271323 | C2 | direct (N × H) |
| 5. C2×#11745158 | C2 | semidirect |
| 6. C2×#11745157 | C2 | semidirect |
| 7. C2×C22⋊#6597 | C2 | semidirect |
| 8. C2×C29×C22⋊Q8 | C2 | semidirect |
| 20. C29×C22⋊Q8 | C22 | semidirect |
| 25. C2×#90785 | C22 | semidirect |
| 27. C2×#90784 | C22 | semidirect |
| 30. C22⋊#6597 | C22 | semidirect |
| 31. #11745158 | C22 | semidirect |
| 32. #11745157 | C22 | semidirect |
| 133. C2×C22⋊Q8 | D29 | semidirect |
| 139. C2×C29 | #452 | semidirect |
| 161. C22⋊Q8 | C2×D29 | semidirect |
| 168. C29 | C2×#452 | semidirect |
| 267. C2 | #14271323 | 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×#90785 | 2 |
| C22×#90784 | 2 |
| #14271323 | 2 |
| C2×#11745158 | 2 |
| C2×#11745157 | 2 |
| C2×C22⋊#6597 | 2 |
| C2×C29×C22⋊Q8 | 2 |
| C2×#452 | 29 |