Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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×#11745311 | C2 | semidirect |
| 2. C2×#11745311 | C2 | semidirect |
| 3. #14271930 | C2 | semidirect |
| 4. #14271431 | C2 | semidirect |
| 5. #14271428 | C2 | semidirect |
| 6. #14271211 | C2 | semidirect |
| 7. #14271147 | C2 | semidirect |
| 8. C2×#11745171 | C2 | semidirect |
| 9. C29×#575 | C2 | semidirect |
| 14. C29×#137 | C22 | semidirect |
| 16. C29×AGL(1,ℤ/8) | C22 | semidirect |
| 24. #11745310 | C22 | semidirect |
| 26. C2×#90784 | C22 | semidirect |
| 28. C2×#90782 | C22 | semidirect |
| 33. #11745184 | C22 | semidirect |
| 34. #11745181 | C22 | semidirect |
| 35. #11745171 | C22 | semidirect |
| 36. #11745170 | C22 | semidirect |
| 141. #575 | D29 | semidirect |
| 161. #137 | C2×D29 | semidirect |
| 167. AGL(1,ℤ/8) | C2×D29 | semidirect |
| 184. C29 | #3068 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745311 | 2 |
| #14271930 | 2 |
| #14271431 | 2 |
| #14271428 | 2 |
| #14271211 | 2 |
| #14271147 | 2 |
| C2×#11745171 | 2 |
| C29×#575 | 2 |
| #3068 | 29 |