Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11745304 | C2 | semidirect |
| 3. C22×#90785 | C2 | semidirect |
| 4. #14271323 | C2 | semidirect |
| 5. #14271318 | C2 | semidirect |
| 6. #14271171 | C2 | semidirect |
| 7. #14271157 | C2 | semidirect |
| 8. #14271130 | C2 | semidirect |
| 9. C29×#536 | C2 | semidirect |
| 139. #536 | D29 | semidirect |
| 177. C29 | #3011 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745365 | 2 |
| C2×#11745304 | 2 |
| C22×#90785 | 2 |
| #14271323 | 2 |
| #14271318 | 2 |
| #14271171 | 2 |
| #14271157 | 2 |
| #14271130 | 2 |
| C29×#536 | 2 |
| #3011 | 29 |