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. #14271929 | C2 | semidirect |
| 4. #14271430 | C2 | semidirect |
| 5. #14271423 | C2 | semidirect |
| 6. #14271212 | C2 | semidirect |
| 7. #14271147 | C2 | semidirect |
| 8. C2×#11745181 | C2 | semidirect |
| 9. C2×C29×AGL(1,ℤ/8) | C2 | semidirect |
| 15. C2×SD16×C29 | C22 | semidirect |
| 16. C2×D8×C29 | C22 | semidirect |
| 21. #11745304 | C22 | semidirect |
| 25. #11745294 | C22 | semidirect |
| 32. #11745263 | C22 | semidirect |
| 33. #11745184 | C22 | semidirect |
| 34. #11745181 | C22 | semidirect |
| 35. #11745181 | C22 | semidirect |
| 36. #11745167 | C22 | semidirect |
| 143. C2×AGL(1,ℤ/8) | D29 | semidirect |
| 170. C2×SD16 | C2×D29 | semidirect |
| 172. C2×D8 | 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 |
|---|---|
| #14271961 | 2 |
| C2×#11745294 | 2 |
| #14271929 | 2 |
| #14271430 | 2 |
| #14271423 | 2 |
| #14271212 | 2 |
| #14271147 | 2 |
| C2×#11745181 | 2 |
| C2×C29×AGL(1,ℤ/8) | 2 |
| #3068 | 29 |