Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
418 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 133 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. #14271487 | C2 | semidirect |
| 3. #14271487 | C2 | semidirect |
| 4. #14271481 | C2 | semidirect |
| 5. #14271476 | C2 | semidirect |
| 6. #14271203 | C2 | semidirect |
| 7. #14271199 | C2 | semidirect |
| 8. #14271167 | C2 | semidirect |
| 9. C2×#11745157 | C2 | semidirect |
| 10. #14271130 | C2 | semidirect |
| 11. C29×#520 | C2 | semidirect |
| 18. C29×#117 | C22 | semidirect |
| 20. C2×C4⋊C4×C29 | C22 | semidirect |
| 29. C22⋊#6597 | C22 | semidirect |
| 30. C22⋊#6597 | C22 | semidirect |
| 35. #11745156 | C22 | semidirect |
| 36. #11745156 | C22 | semidirect |
| 37. #11745156 | C22 | semidirect |
| 38. #11745155 | C22 | semidirect |
| 39. #11745155 | C22 | semidirect |
| 40. #11745155 | C22 | semidirect |
| 130. #520 | D29 | semidirect |
| 160. #117 | C2×D29 | semidirect |
| 162. C2×C4⋊C4 | C2×D29 | semidirect |
| 175. C29 | #3096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271727 | 2 |
| #14271487 | 2 |
| #14271481 | 2 |
| #14271476 | 2 |
| #14271203 | 2 |
| #14271199 | 2 |
| #14271167 | 2 |
| C2×#11745157 | 2 |
| #14271130 | 2 |
| C29×#520 | 2 |
| #3096 | 29 |