Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
592 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#90785 | C2 | semidirect |
| 2. C22×#90773 | C2 | semidirect |
| 4. C2×#11745309 | C2 | semidirect |
| 5. C2×#11745298 | C2 | semidirect |
| 6. #14271544 | C2 | direct (N × H) |
| 7. C2×C8×Dic29 | C2 | semidirect |
| 8. C22×SD16×C29 | C2 | semidirect |
| 14. C2×SD16×C29 | C22 | semidirect |
| 18. #11745309 | C22 | semidirect |
| 20. C2×#90785 | C22 | semidirect |
| 22. #11745298 | C22 | semidirect |
| 29. C2×#90773 | C22 | semidirect |
| 30. C8×Dic29 | C22 | semidirect |
| 114. C22×SD16 | D29 | semidirect |
| 121. C2×C29 | #495 | semidirect |
| 134. C2×SD16 | C2×D29 | semidirect |
| 147. C29 | C2×#495 | semidirect |
| 230. C2 | #14271544 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90785 | 2 |
| C22×#90773 | 2 |
| C22×#90782 | 2 |
| C2×#11745309 | 2 |
| C2×#11745298 | 2 |
| #14271544 | 2 |
| C2×C8×Dic29 | 2 |
| C22×SD16×C29 | 2 |
| C2×#495 | 29 |