Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#11745294 | C2 | semidirect |
| 2. C2×#11745310 | C2 | semidirect |
| 3. #14271741 | C2 | semidirect |
| 4. #14271414 | C2 | semidirect |
| 5. #14271407 | C2 | semidirect |
| 6. #14271397 | C2 | semidirect |
| 7. #14271390 | C2 | semidirect |
| 8. #14271206 | C2 | semidirect |
| 9. #14271157 | C2 | semidirect |
| 10. C2×#11745180 | C2 | semidirect |
| 11. C29×#535 | C2 | semidirect |
| 28. #11745292 | C22 | semidirect |
| 30. #11745286 | C22 | semidirect |
| 32. C2×#90777 | C22 | semidirect |
| 34. C22×#6597 | C22 | semidirect |
| 37. #11745158 | C22 | semidirect |
| 38. #11745158 | C22 | semidirect |
| 39. #11745157 | C22 | semidirect |
| 40. #11745157 | C22 | semidirect |
| 41. #11745156 | C22 | semidirect |
| 42. #11745155 | C22 | semidirect |
| 79. #90777 | D4 | semidirect |
| 148. #535 | D29 | semidirect |
| 194. C29 | #3062 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745294 | 2 |
| C2×#11745310 | 2 |
| #14271741 | 2 |
| #14271414 | 2 |
| #14271407 | 2 |
| #14271397 | 2 |
| #14271390 | 2 |
| #14271206 | 2 |
| #14271157 | 2 |
| C2×#11745180 | 2 |
| C29×#535 | 2 |
| #3062 | 29 |