Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
416 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 153 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 |
|---|---|---|
| 4. #14270918 | C2 | semidirect |
| 5. #14270917 | C2 | semidirect |
| 6. #14270917 | C2 | semidirect |
| 7. C29×#336 | C2 | semidirect |
| 19. C2×#90772 | C4 | semidirect |
| 22. C2×C8×D29 | C4 | semidirect |
| 109. #336 | D29 | semidirect |
| 133. C29 | #1729 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90772 | 2 |
| C22×C8×D29 | 2 |
| C2×#11745234 | 2 |
| #14270918 | 2 |
| #14270917 | 2 |
| C29×#336 | 2 |
| #1729 | 29 |