Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
196 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 129 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. #14270938 | C2 | semidirect |
| 4. C16×Dic29 | C2 | semidirect |
| 9. C29×M32 | C4 | semidirect |
| 15. #11745160 | C4 | semidirect |
| 29. C16×C29 | C2×C4 | semidirect |
| 30. #90768 | C2×C4 | semidirect |
| 52. Dic29 | M32 | direct (N × H) |
| 65. M32 | Dic29 | direct (N × H) |
| 72. C29 | C4×M32 | semidirect |
| 86. C16 | C2×Dic29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745160 | 2 |
| C2×C8×Dic29 | 2 |
| #14270938 | 2 |
| C16×Dic29 | 2 |
| C2×C29×M32 | 2 |
| C4×M32 | 29 |