Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
448 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 117 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. #14271979 | C2 | semidirect |
| 2. #14271974 | C2 | semidirect |
| 3. #14271558 | C2 | semidirect |
| 4. #14271436 | C2 | semidirect |
| 5. #14271425 | C2 | semidirect |
| 6. #14271347 | C2 | semidirect |
| 7. #14271335 | C2 | semidirect |
| 8. #14271282 | C2 | semidirect |
| 9. C29×#455 | C2 | semidirect |
| 12. #11745362 | C22 | semidirect |
| 20. C2×#90785 | C22 | semidirect |
| 29. #11745271 | C22 | semidirect |
| 30. #11745269 | C22 | semidirect |
| 31. #11745231 | C22 | semidirect |
| 34. #11745184 | C22 | semidirect |
| 35. #11745172 | C22 | semidirect |
| 36. #11745170 | C22 | semidirect |
| 37. #11745153 | C22 | semidirect |
| 38. #11745151 | C22 | semidirect |
| 131. #455 | D29 | semidirect |
| 168. C29 | #3289 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271979 | 2 |
| #14271974 | 2 |
| #14271558 | 2 |
| #14271436 | 2 |
| #14271425 | 2 |
| #14271347 | 2 |
| #14271335 | 2 |
| #14271282 | 2 |
| C29×#455 | 2 |
| #3289 | 29 |