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. #14271054 | C2 | semidirect |
| 4. #14271053 | C2 | semidirect |
| 5. #14271051 | C2 | semidirect |
| 6. #14271043 | C2 | semidirect |
| 7. #14271040 | C2 | semidirect |
| 8. #14271018 | C2 | semidirect |
| 9. C29×#390 | C2 | semidirect |
| 13. C23×Dic29 | C22 | semidirect |
| 14. C2×C4⋊C4×C29 | C22 | semidirect |
| 16. C2×C22⋊C4×C29 | C22 | semidirect |
| 17. C2×C42×C29 | C22 | semidirect |
| 20. C2×C22⋊Dic29 | C22 | semidirect |
| 21. #11745299 | C4 | semidirect |
| 27. C2×#90779 | C22 | semidirect |
| 28. C2×C4×Dic29 | C22 | semidirect |
| 29. #11745179 | C22 | semidirect |
| 30. #11745179 | C22 | semidirect |
| 31. #11745179 | C22 | semidirect |
| 38. C23×D29 | C2×C4 | semidirect |
| 60. C22⋊Dic29 | C2×C4 | semidirect |
| 65. #90781 | C2×C4 | semidirect |
| 144. #390 | D29 | semidirect |
| 165. C2×C4⋊C4 | C2×D29 | semidirect |
| 175. C2×C22⋊C4 | C2×D29 | semidirect |
| 177. C2×C42 | C2×D29 | semidirect |
| 181. C29 | #2375 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745299 | 2 |
| #14271063 | 2 |
| #14271054 | 2 |
| #14271053 | 2 |
| #14271051 | 2 |
| #14271043 | 2 |
| #14271040 | 2 |
| #14271018 | 2 |
| C29×#390 | 2 |
| #2375 | 29 |