Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
462 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 137 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×#11745288 | C2 | semidirect |
| 3. #14271488 | C2 | semidirect |
| 4. #14271482 | C2 | semidirect |
| 5. #14271477 | C2 | semidirect |
| 6. #14271205 | C2 | semidirect |
| 7. #14271169 | C2 | semidirect |
| 8. C29×#407 | C2 | semidirect |
| 22. #11745288 | C22 | semidirect |
| 24. C2×C4⋊Dic29 | C22 | semidirect |
| 25. C2×C4⋊Dic29 | C22 | semidirect |
| 27. C29×C22⋊C8 | C22 | semidirect |
| 28. C29×C22⋊C8 | C22 | semidirect |
| 29. #11745169 | C22 | semidirect |
| 30. #11745169 | C22 | semidirect |
| 31. #11745166 | C22 | semidirect |
| 32. #11745165 | C22 | semidirect |
| 126. #407 | D29 | semidirect |
| 156. C22⋊C8 | C2×D29 | semidirect |
| 157. C22⋊C8 | C2×D29 | semidirect |
| 158. C29 | #3094 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745292 | 2 |
| C2×#11745288 | 2 |
| #14271488 | 2 |
| #14271482 | 2 |
| #14271477 | 2 |
| #14271205 | 2 |
| #14271169 | 2 |
| C29×#407 | 2 |
| #3094 | 29 |