Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
688 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 173 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. #14271063 | C2 | semidirect |
| 3. #14271057 | C2 | semidirect |
| 4. #14271051 | C2 | semidirect |
| 5. #14271039 | C2 | semidirect |
| 6. #14271019 | C2 | semidirect |
| 7. C29×#379 | C2 | semidirect |
| 10. C22×C4×D29 | C22 | semidirect |
| 13. #11745315 | C4 | semidirect |
| 17. C2×#90781 | C22 | semidirect |
| 18. C2×#90779 | C22 | semidirect |
| 19. C2×C4×Dic29 | C22 | semidirect |
| 20. #11745179 | C22 | semidirect |
| 21. #11745179 | C22 | semidirect |
| 24. C24×C29 | C2×C4 | semidirect |
| 40. C22⋊Dic29 | C2×C4 | semidirect |
| 97. #379 | D29 | semidirect |
| 117. C29 | #2375 | semidirect |
| 121. C24 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745315 | 2 |
| #14271063 | 2 |
| #14271057 | 2 |
| #14271051 | 2 |
| #14271039 | 2 |
| #14271019 | 2 |
| C29×#379 | 2 |
| #2375 | 29 |