Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
448 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 3. C22×#90785 | C2 | semidirect |
| 5. #14271437 | C2 | direct (N × H) |
| 6. C2×#11745170 | C2 | semidirect |
| 7. C2×#11745172 | C2 | semidirect |
| 8. C2×C29×#101 | C2 | semidirect |
| 18. C2×#90785 | C22 | semidirect |
| 32. C29×#101 | C22 | semidirect |
| 33. #11745172 | C22 | semidirect |
| 34. #11745170 | C22 | semidirect |
| 136. C2×#101 | D29 | semidirect |
| 139. C2×C29 | #473 | semidirect |
| 167. #101 | C2×D29 | semidirect |
| 168. C29 | C2×#473 | semidirect |
| 265. C2 | #14271437 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745271 | 2 |
| C2×#11745304 | 2 |
| C22×#90785 | 2 |
| C2×#11745269 | 2 |
| #14271437 | 2 |
| C2×#11745170 | 2 |
| C2×#11745172 | 2 |
| C2×C29×#101 | 2 |
| C2×#473 | 29 |