Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
368 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 368 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 |
|---|---|---|
| 2. C2×#11745182 | C2 | semidirect |
| 3. #14270955 | C2 | direct (N × H) |
| 4. C2×C29×#99 | C2 | semidirect |
| 8. C22×D116 | C4 | semidirect |
| 13. #11745302 | C4 | semidirect |
| 15. C2×C4×Dic29 | C4 | semidirect |
| 17. C29×#99 | C22 | semidirect |
| 19. #11745182 | C22 | semidirect |
| 42. C2×D116 | C2×C4 | semidirect |
| 48. C4×Dic29 | C2×C4 | semidirect |
| 114. C2×#99 | D29 | semidirect |
| 122. C2×C29 | #353 | semidirect |
| 139. #99 | C2×D29 | semidirect |
| 140. C29 | C2×#353 | semidirect |
| 239. C2 | #14270955 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745302 | 2 |
| C2×#11745182 | 2 |
| #14270955 | 2 |
| C2×C29×#99 | 2 |
| C2×#353 | 29 |