Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
232 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 85 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×#11745165 | C2 | semidirect |
| 3. #14270974 | C2 | direct (N × H) |
| 4. C2×C29×M32 | C2 | semidirect |
| 8. C2×Dic116 | C4 | semidirect |
| 11. #11745266 | C4 | semidirect |
| 13. C2×D232 | C4 | semidirect |
| 16. C29×M32 | C22 | semidirect |
| 19. #11745165 | C22 | semidirect |
| 39. Dic116 | C2×C4 | semidirect |
| 41. D232 | C2×C4 | semidirect |
| 82. C2×M32 | D29 | semidirect |
| 87. C2×C29 | #360 | semidirect |
| 101. M32 | C2×D29 | semidirect |
| 105. C29 | C2×#360 | semidirect |
| 169. C2 | #14270974 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745266 | 2 |
| C2×#11745165 | 2 |
| #14270974 | 2 |
| C2×C29×M32 | 2 |
| C2×#360 | 29 |