Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 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. #14271284 | C2 | semidirect |
| 3. #14271274 | C2 | semidirect |
| 4. #14270975 | C2 | semidirect |
| 5. #14270972 | C2 | semidirect |
| 6. #14270940 | C2 | semidirect |
| 7. C29×#365 | C2 | semidirect |
| 19. #11745148 | C4 | semidirect |
| 20. D464 | C4 | semidirect |
| 30. Dic116 | C2×C4 | semidirect |
| 33. D232 | C2×C4 | semidirect |
| 37. C16×C29 | C2×C4 | semidirect |
| 68. #365 | 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 |
| #14271284 | 2 |
| #14271274 | 2 |
| #14270975 | 2 |
| #14270972 | 2 |
| #14270940 | 2 |
| C29×#365 | 2 |
| AGL(1,ℤ/16) | 29 |