Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
792 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 229 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×C8×D29 | C2 | semidirect |
| 3. C2×#11745254 | C2 | semidirect |
| 4. #14271156 | C2 | direct (N × H) |
| 5. C2×#11745164 | C2 | semidirect |
| 6. C2×#11745158 | C2 | semidirect |
| 7. C2×#11745180 | C2 | semidirect |
| 8. C2×C29×#102 | C2 | semidirect |
| 14. C2×#90807 | C4 | semidirect |
| 25. C2×C8×D29 | C22 | semidirect |
| 27. #11745254 | C22 | semidirect |
| 28. C29×#102 | C22 | semidirect |
| 29. #11745180 | C22 | semidirect |
| 30. #11745164 | C22 | semidirect |
| 31. #11745158 | C22 | semidirect |
| 49. #90807 | C2×C4 | semidirect |
| 130. C2×#102 | D29 | semidirect |
| 132. C2×C29 | #416 | semidirect |
| 159. #102 | C2×D29 | semidirect |
| 160. C29 | C2×#416 | semidirect |
| 253. C2 | #14271156 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90807 | 2 |
| C22×C8×D29 | 2 |
| C2×#11745254 | 2 |
| #14271156 | 2 |
| C2×#11745164 | 2 |
| C2×#11745158 | 2 |
| C2×#11745180 | 2 |
| C2×C29×#102 | 2 |
| C2×#416 | 29 |