Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
278 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 69 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. #14270954 | C2 | direct (N × H) |
| 6. C23×Dic29 | C4 | semidirect |
| 10. C2×C22⋊Dic29 | C4 | semidirect |
| 13. #11745297 | C4 | semidirect |
| 35. C22×Dic29 | C2×C4 | semidirect |
| 44. C22⋊Dic29 | C2×C4 | semidirect |
| 108. C2×C29 | #352 | semidirect |
| 125. C29 | C2×#352 | semidirect |
| 209. C2 | #14270954 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745297 | 2 |
| C2×#11745182 | 2 |
| #14270954 | 2 |
| C2×C29×#100 | 2 |
| C2×#352 | 29 |