Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
736 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 1. #14271999 | C2 | semidirect |
| 2. C2×#11745294 | C2 | semidirect |
| 3. #14271335 | C2 | semidirect |
| 4. #14271330 | C2 | semidirect |
| 5. #14271181 | C2 | semidirect |
| 6. #14271147 | C2 | semidirect |
| 7. C29×#535 | C2 | semidirect |
| 9. C22×D4×C29 | C22 | semidirect |
| 13. #11745362 | C22 | semidirect |
| 15. #11745359 | C22 | semidirect |
| 18. C29×#127 | C22 | semidirect |
| 19. C29×#124 | C22 | semidirect |
| 22. C29×#117 | C22 | semidirect |
| 25. #11745294 | C22 | semidirect |
| 27. C2×#90777 | C22 | semidirect |
| 28. #11745184 | C22 | semidirect |
| 29. #11745181 | C22 | semidirect |
| 30. #11745153 | C22 | semidirect |
| 57. #90805 | D4 | semidirect |
| 60. C2×D116 | D4 | semidirect |
| 64. C2×Dic58 | D4 | semidirect |
| 131. #535 | D29 | semidirect |
| 151. C22×D4 | C2×D29 | semidirect |
| 157. #127 | C2×D29 | semidirect |
| 158. #124 | C2×D29 | semidirect |
| 161. #117 | C2×D29 | semidirect |
| 165. C29 | #3021 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271999 | 2 |
| C2×#11745294 | 2 |
| #14271335 | 2 |
| #14271330 | 2 |
| #14271181 | 2 |
| #14271147 | 2 |
| C29×#535 | 2 |
| #3021 | 29 |