Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
754 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 153 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×#11745271 | C2 | semidirect |
| 3. C2×#11745286 | C2 | semidirect |
| 4. #14271327 | C2 | semidirect |
| 5. #14271321 | C2 | semidirect |
| 6. #14271316 | C2 | semidirect |
| 7. #14271165 | C2 | semidirect |
| 8. C29×#407 | C2 | semidirect |
| 19. C22×Dic58 | C22 | semidirect |
| 20. C2×M16×C29 | C22 | semidirect |
| 22. C2×C4⋊Dic29 | C22 | semidirect |
| 26. #11745286 | C22 | semidirect |
| 29. C2×Dic116 | C22 | semidirect |
| 30. C2×#90773 | C22 | semidirect |
| 32. C29×C22⋊C8 | C22 | semidirect |
| 33. #11745169 | C22 | semidirect |
| 34. #11745164 | C22 | semidirect |
| 127. C22×C29 | #137 | semidirect |
| 147. #407 | D29 | semidirect |
| 169. C2×M16 | C2×D29 | semidirect |
| 180. C22⋊C8 | C2×D29 | semidirect |
| 181. C29 | #3007 | semidirect |
| 277. C22 | #11745271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90805 | 2 |
| C2×#11745271 | 2 |
| C2×#11745286 | 2 |
| #14271327 | 2 |
| #14271321 | 2 |
| #14271316 | 2 |
| #14271165 | 2 |
| C29×#407 | 2 |
| #3007 | 29 |