Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
224 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 81 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. #14271201 | C2 | semidirect |
| 3. #14270974 | C2 | semidirect |
| 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 |
| 81. C2×M32 | D29 | semidirect |
| 100. M32 | C2×D29 | semidirect |
| 104. C29 | #2145 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745266 | 2 |
| #14271201 | 2 |
| #14270974 | 2 |
| C2×C29×M32 | 2 |
| #2145 | 29 |