Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
492 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 135 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×Q16×D29 | C2 | semidirect |
| 4. #14271422 | C2 | semidirect |
| 5. #14271421 | C2 | semidirect |
| 6. #14271420 | C2 | semidirect |
| 7. #14271419 | C2 | semidirect |
| 8. #14271418 | C2 | semidirect |
| 9. #106×D29 | C2 | semidirect |
| 10. #103×D29 | C2 | semidirect |
| 11. C29×#470 | C2 | semidirect |
| 14. C2×Q16×C29 | C22 | semidirect |
| 18. C2×#90785 | C22 | semidirect |
| 23. C2×Dic116 | C22 | semidirect |
| 34. C29×#106 | C22 | semidirect |
| 35. C29×#103 | C22 | semidirect |
| 36. #11745183 | C22 | semidirect |
| 37. #11745165 | C22 | semidirect |
| 38. #11745164 | C22 | semidirect |
| 39. #11745158 | C22 | semidirect |
| 40. #11745156 | C22 | semidirect |
| 140. #470 | D29 | direct (N × H) |
| 147. D29 | #470 | direct (N × H) |
| 153. C2×Q16 | C2×D29 | semidirect |
| 172. #106 | C2×D29 | semidirect |
| 176. #103 | C2×D29 | semidirect |
| 177. C29 | C2×#470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D29 | 2 |
| C2×M16×D29 | 2 |
| C22⋊Q8×D29 | 2 |
| #14271422 | 2 |
| #14271421 | 2 |
| #14271420 | 2 |
| #14271419 | 2 |
| #14271418 | 2 |
| #106×D29 | 2 |
| #103×D29 | 2 |
| C29×#470 | 2 |
| C2×#470 | 29 |