Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
232 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 67 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. M32×D29 | C2 | semidirect |
| 3. #106×D29 | C2 | semidirect |
| 4. #14270974 | C2 | semidirect |
| 5. #14270973 | C2 | semidirect |
| 6. #14270972 | C2 | semidirect |
| 7. C29×#360 | C2 | semidirect |
| 11. #11745281 | C4 | semidirect |
| 12. Q16×D29 | C4 | semidirect |
| 15. #11745274 | C4 | semidirect |
| 16. D8×D29 | C4 | semidirect |
| 20. C29×M32 | C22 | semidirect |
| 21. C29×#106 | C22 | semidirect |
| 22. #11745165 | C22 | semidirect |
| 23. #11745160 | C22 | semidirect |
| 39. Q16×C29 | C2×C4 | semidirect |
| 41. D8×C29 | C2×C4 | semidirect |
| 51. Dic116 | C2×C4 | semidirect |
| 52. D232 | C2×C4 | semidirect |
| 112. #360 | D29 | direct (N × H) |
| 118. D29 | #360 | direct (N × H) |
| 133. M32 | C2×D29 | semidirect |
| 137. #106 | C2×D29 | semidirect |
| 138. C29 | C2×#360 | semidirect |
| 153. Q16 | C4×D29 | semidirect |
| 160. D8 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #135×D29 | 2 |
| M32×D29 | 2 |
| #106×D29 | 2 |
| #14270974 | 2 |
| #14270973 | 2 |
| #14270972 | 2 |
| C29×#360 | 2 |
| C2×#360 | 29 |