Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
448 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 125 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. #14271715 | C2 | semidirect |
| 3. #14271493 | C2 | semidirect |
| 4. #14271452 | C2 | semidirect |
| 5. #14271367 | C2 | semidirect |
| 8. #14271250 | C2 | semidirect |
| 9. #14271248 | C2 | semidirect |
| 10. #14271213 | C2 | semidirect |
| 11. C29×#483 | C2 | semidirect |
| 16. Q8×Dic29 | C22 | semidirect |
| 17. #11745306 | C22 | semidirect |
| 28. #11745250 | C22 | semidirect |
| 30. #11745249 | C22 | semidirect |
| 33. C29×#106 | C22 | semidirect |
| 34. C29×#103 | C22 | semidirect |
| 38. #11745162 | C22 | semidirect |
| 39. C8×Dic29 | C22 | semidirect |
| 40. #11745158 | C22 | semidirect |
| 42. #11745156 | C22 | semidirect |
| 98. C2×Dic29 | SD16 | semidirect |
| 135. #483 | D29 | semidirect |
| 170. #106 | C2×D29 | semidirect |
| 173. #103 | C2×D29 | semidirect |
| 179. C29 | #3101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271715 | 2 |
| C2×#11745255 | 2 |
| #14271493 | 2 |
| #14271452 | 2 |
| #14271367 | 2 |
| #14271316 | 2 |
| #14271313 | 2 |
| #14271250 | 2 |
| #14271248 | 2 |
| #14271213 | 2 |
| C29×#483 | 2 |
| #3101 | 29 |