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. #14271961 | C2 | semidirect |
| 2. C2×#11745294 | C2 | semidirect |
| 3. #14271930 | C2 | semidirect |
| 4. #14271431 | C2 | semidirect |
| 5. #14271424 | C2 | semidirect |
| 6. #14271211 | C2 | semidirect |
| 7. #14271145 | C2 | semidirect |
| 8. C2×#11745181 | C2 | semidirect |
| 9. C2×C29×AGL(1,ℤ/8) | C2 | semidirect |
| 18. #11745313 | C22 | semidirect |
| 20. #11745311 | C22 | semidirect |
| 22. #11745310 | C22 | semidirect |
| 24. C2×#90783 | C22 | semidirect |
| 28. C2×#90782 | C22 | semidirect |
| 33. #11745181 | C22 | semidirect |
| 34. #11745172 | C22 | semidirect |
| 35. #11745171 | C22 | semidirect |
| 36. #11745170 | C22 | semidirect |
| 143. C2×AGL(1,ℤ/8) | 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 |
|---|---|
| #14271961 | 2 |
| C2×#11745294 | 2 |
| #14271930 | 2 |
| #14271431 | 2 |
| #14271424 | 2 |
| #14271211 | 2 |
| #14271145 | 2 |
| C2×#11745181 | 2 |
| C2×C29×AGL(1,ℤ/8) | 2 |
| #3068 | 29 |