Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
418 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 133 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. #14271646 | C2 | semidirect |
| 3. #14271488 | C2 | semidirect |
| 4. #14271488 | C2 | semidirect |
| 5. #14271482 | C2 | semidirect |
| 6. #14271477 | C2 | semidirect |
| 7. #14271205 | C2 | semidirect |
| 8. #14271201 | C2 | semidirect |
| 9. #14271169 | C2 | semidirect |
| 10. C2×#11745169 | C2 | semidirect |
| 11. C29×#408 | C2 | semidirect |
| 26. #11745288 | C22 | semidirect |
| 28. C2×C4⋊Dic29 | C22 | semidirect |
| 29. C29×C22⋊C8 | C22 | semidirect |
| 30. C29×C22⋊C8 | C22 | semidirect |
| 35. #11745166 | C22 | semidirect |
| 36. #11745166 | C22 | semidirect |
| 37. #11745166 | C22 | semidirect |
| 38. #11745165 | C22 | semidirect |
| 39. #11745165 | C22 | semidirect |
| 40. #11745165 | C22 | semidirect |
| 139. #408 | D29 | semidirect |
| 173. C22⋊C8 | C2×D29 | semidirect |
| 174. C22⋊C8 | C2×D29 | semidirect |
| 175. C29 | #3096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271727 | 2 |
| #14271646 | 2 |
| #14271488 | 2 |
| #14271482 | 2 |
| #14271477 | 2 |
| #14271205 | 2 |
| #14271201 | 2 |
| #14271169 | 2 |
| C2×#11745169 | 2 |
| C29×#408 | 2 |
| #3096 | 29 |