Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
154 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 53 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. #14271286 | C2 | semidirect |
| 3. #14271276 | C2 | semidirect |
| 4. #14270986 | C2 | semidirect |
| 5. #14270977 | C2 | semidirect |
| 6. #14270974 | C2 | semidirect |
| 7. C29×#347 | C2 | semidirect |
| 19. #11745148 | C4 | semidirect |
| 20. D464 | C4 | semidirect |
| 30. Dic116 | C2×C4 | semidirect |
| 33. D232 | C2×C4 | semidirect |
| 38. C16×C29 | C2×C4 | semidirect |
| 71. #347 | D29 | semidirect |
| 89. C29 | AGL(1,ℤ/16) | semidirect |
| 107. C16 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271601 | 2 |
| #14271286 | 2 |
| #14271276 | 2 |
| #14270986 | 2 |
| #14270977 | 2 |
| #14270974 | 2 |
| C29×#347 | 2 |
| AGL(1,ℤ/16) | 29 |