Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
800 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 209 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. #14271637 | C2 | semidirect |
| 3. #14271137 | C2 | semidirect |
| 4. #14271136 | C2 | semidirect |
| 5. #99×D29 | C2 | semidirect |
| 6. C29×#410 | C2 | semidirect |
| 10. C2×#90809 | C4 | semidirect |
| 11. C2×D4×D29 | C4 | semidirect |
| 13. C2×#90805 | C4 | semidirect |
| 15. C22×D116 | C4 | semidirect |
| 17. C29×#117 | C22 | semidirect |
| 18. #11745288 | C22 | semidirect |
| 20. C22⋊C4×D29 | C22 | semidirect |
| 22. C29×#99 | C22 | semidirect |
| 23. #11745182 | C22 | semidirect |
| 24. #11745154 | C22 | semidirect |
| 25. C23×D29 | C2×C4 | semidirect |
| 29. C2×Q8×C29 | C2×C4 | semidirect |
| 30. C2×D4×C29 | C2×C4 | semidirect |
| 32. C22×C4×C29 | C2×C4 | semidirect |
| 34. C2×C22⋊D29 | C2×C4 | semidirect |
| 47. C2×D116 | C2×C4 | semidirect |
| 48. C2×D116 | C2×C4 | semidirect |
| 52. C2×C4×D29 | C2×C4 | semidirect |
| 53. C2×C4×D29 | C2×C4 | semidirect |
| 54. C2×Dic58 | C2×C4 | semidirect |
| 119. #410 | D29 | semidirect |
| 140. #117 | C2×D29 | semidirect |
| 144. #99 | C2×D29 | semidirect |
| 145. C29 | #2883 | semidirect |
| 156. C2×Q8 | C4×D29 | semidirect |
| 169. C2×D4 | C4×D29 | semidirect |
| 174. C22×C4 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745364 | 2 |
| #14271637 | 2 |
| #14271137 | 2 |
| #14271136 | 2 |
| #99×D29 | 2 |
| C29×#410 | 2 |
| #2883 | 29 |