Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
360 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 119 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. M16×Dic29 | C2 | semidirect |
| 4. #14270931 | C2 | semidirect |
| 15. C29×#100 | C4 | semidirect |
| 16. #11745181 | C4 | semidirect |
| 32. M16×C29 | C2×C4 | semidirect |
| 39. #90777 | C2×C4 | semidirect |
| 80. Dic29 | #100 | direct (N × H) |
| 102. #100 | Dic29 | direct (N × H) |
| 105. C29 | C4×#100 | semidirect |
| 121. M16 | C2×Dic29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic29 | 2 |
| C2×#11745181 | 2 |
| M16×Dic29 | 2 |
| #14270931 | 2 |
| C2×C29×#100 | 2 |
| C4×#100 | 29 |