Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
792 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 269 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. C23×#6597 | C2 | semidirect |
| 3. #14271157 | C2 | direct (N × H) |
| 4. C2×#11745158 | C2 | semidirect |
| 5. C2×#11745157 | C2 | semidirect |
| 6. C2×C29×#117 | C2 | semidirect |
| 11. C2×#90805 | C4 | semidirect |
| 17. C29×#117 | C22 | semidirect |
| 23. C22×#6597 | C22 | semidirect |
| 24. #11745158 | C22 | semidirect |
| 25. #11745157 | C22 | semidirect |
| 40. #90805 | C2×C4 | semidirect |
| 105. C2×#117 | D29 | semidirect |
| 110. C2×C29 | #416 | semidirect |
| 127. #117 | C2×D29 | semidirect |
| 133. C29 | C2×#416 | semidirect |
| 212. C2 | #14271157 | 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 |
| C23×#6597 | 2 |
| #14271157 | 2 |
| C2×#11745158 | 2 |
| C2×#11745157 | 2 |
| C2×C29×#117 | 2 |
| C2×#416 | 29 |