Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
166 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 71 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. #14270916 | C2 | semidirect |
| 5. #14270915 | C2 | semidirect |
| 6. #14270913 | C2 | semidirect |
| 7. C29×#334 | C2 | semidirect |
| 56. C8×C29 | M16 | semidirect |
| 60. #6597 | M16 | semidirect |
| 80. #334 | D29 | semidirect |
| 100. C29 | #1569 | semidirect |
| 138. C8 | #90772 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271219 | 2 |
| #14271185 | 2 |
| C4×#90772 | 2 |
| #14270916 | 2 |
| #14270915 | 2 |
| #14270913 | 2 |
| C29×#334 | 2 |
| #1569 | 29 |