Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 1. #14271963 | C2 | semidirect |
| 2. C2×#11745270 | C2 | semidirect |
| 3. C2×#11745270 | C2 | semidirect |
| 4. #14271929 | C2 | semidirect |
| 5. #14271434 | C2 | semidirect |
| 6. #14271427 | C2 | semidirect |
| 7. #14271145 | C2 | semidirect |
| 8. C2×#11745171 | C2 | semidirect |
| 9. C29×#430 | C2 | semidirect |
| 18. #11745271 | C22 | semidirect |
| 24. #11745270 | C22 | semidirect |
| 29. C2×D232 | C22 | semidirect |
| 31. C2×#90773 | C22 | semidirect |
| 32. #11745263 | C22 | semidirect |
| 33. C29×#108 | C22 | semidirect |
| 34. #11745172 | C22 | semidirect |
| 35. #11745171 | C22 | semidirect |
| 36. #11745171 | C22 | semidirect |
| 147. #430 | D29 | semidirect |
| 180. #108 | C2×D29 | semidirect |
| 184. C29 | #3068 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271963 | 2 |
| C2×#11745270 | 2 |
| #14271929 | 2 |
| #14271434 | 2 |
| #14271427 | 2 |
| #14271145 | 2 |
| C2×#11745171 | 2 |
| C29×#430 | 2 |
| #3068 | 29 |