Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
278 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 77 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. #14270953 | C2 | direct (N × H) |
| 6. C23×C4×C29 | C4 | semidirect |
| 9. C29×#123 | C4 | semidirect |
| 13. C2×C22⋊C4×C29 | C4 | semidirect |
| 33. C22×C4×C29 | C2×C4 | semidirect |
| 41. C22⋊C4×C29 | C2×C4 | semidirect |
| 108. C2×C29 | #352 | semidirect |
| 111. C23×C4 | Dic29 | semidirect |
| 115. #123 | Dic29 | semidirect |
| 120. C2×C22⋊C4 | Dic29 | semidirect |
| 125. C29 | C2×#352 | semidirect |
| 140. C22×C4 | C2×Dic29 | semidirect |
| 152. C22⋊C4 | C2×Dic29 | semidirect |
| 209. C2 | #14270953 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745181 | 2 |
| C2×#11745182 | 2 |
| #14270953 | 2 |
| C2×C29×#123 | 2 |
| C2×#352 | 29 |