Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 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 |
|---|---|---|
| 1. C2×#11745270 | C2 | semidirect |
| 2. C2×#11745312 | C2 | semidirect |
| 3. #14271727 | C2 | semidirect |
| 4. #14271644 | C2 | semidirect |
| 5. #14271388 | C2 | semidirect |
| 6. #14271381 | C2 | semidirect |
| 7. #14271362 | C2 | semidirect |
| 8. #14271357 | C2 | semidirect |
| 9. #14271191 | C2 | semidirect |
| 10. C2×#11745157 | C2 | semidirect |
| 11. C29×#417 | C2 | semidirect |
| 19. C2×#90785 | C22 | semidirect |
| 20. C2×#90784 | C22 | semidirect |
| 23. C2×#90783 | C22 | semidirect |
| 24. C2×#90782 | C22 | semidirect |
| 33. #11745255 | C22 | semidirect |
| 36. #11745249 | C22 | semidirect |
| 37. C29×#103 | C22 | semidirect |
| 38. C29×#102 | C22 | semidirect |
| 39. #11745162 | C22 | semidirect |
| 40. #11745162 | C22 | semidirect |
| 56. #90805 | D4 | semidirect |
| 157. #417 | D29 | semidirect |
| 193. #103 | C2×D29 | semidirect |
| 196. #102 | C2×D29 | semidirect |
| 197. C29 | #3045 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745270 | 2 |
| C2×#11745312 | 2 |
| #14271727 | 2 |
| #14271644 | 2 |
| #14271388 | 2 |
| #14271381 | 2 |
| #14271362 | 2 |
| #14271357 | 2 |
| #14271191 | 2 |
| C2×#11745157 | 2 |
| C29×#417 | 2 |
| #3045 | 29 |