Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
446 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 446 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 |
|---|---|---|
| 2. C2×#11745304 | C2 | semidirect |
| 3. #14271930 | C2 | semidirect |
| 4. #14271436 | C2 | semidirect |
| 5. #14271428 | C2 | semidirect |
| 6. #14271211 | C2 | semidirect |
| 7. #14271145 | C2 | semidirect |
| 8. C2×#11745184 | C2 | semidirect |
| 9. C2×C29×#137 | C2 | semidirect |
| 23. C2×#90785 | C22 | semidirect |
| 27. C2×#90784 | C22 | semidirect |
| 33. #11745184 | C22 | semidirect |
| 34. #11745172 | C22 | semidirect |
| 35. #11745171 | C22 | semidirect |
| 36. #11745170 | C22 | semidirect |
| 139. C2×#137 | D29 | semidirect |
| 179. C29 | #3069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271961 | 2 |
| C2×#11745304 | 2 |
| #14271930 | 2 |
| #14271436 | 2 |
| #14271428 | 2 |
| #14271211 | 2 |
| #14271145 | 2 |
| C2×#11745184 | 2 |
| C2×C29×#137 | 2 |
| #3069 | 29 |