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×#11745294 | C2 | semidirect |
| 2. C2×#11745266 | C2 | semidirect |
| 3. #14271730 | C2 | semidirect |
| 4. #14271644 | C2 | semidirect |
| 5. #14271384 | C2 | semidirect |
| 6. #14271377 | C2 | semidirect |
| 7. #14271362 | C2 | semidirect |
| 8. #14271357 | C2 | semidirect |
| 9. #14271189 | C2 | semidirect |
| 10. #14271162 | C2 | semidirect |
| 11. C2×C29×#102 | C2 | semidirect |
| 28. C2×Dic116 | C22 | semidirect |
| 30. C2×D232 | C22 | semidirect |
| 31. C2×#90773 | C22 | semidirect |
| 32. C2×#90773 | C22 | semidirect |
| 33. #11745255 | C22 | semidirect |
| 36. #11745249 | C22 | semidirect |
| 39. #11745162 | C22 | semidirect |
| 40. #11745162 | C22 | semidirect |
| 41. #11745158 | C22 | semidirect |
| 42. #11745157 | C22 | semidirect |
| 57. #90805 | D4 | semidirect |
| 158. C2×#102 | 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×#11745294 | 2 |
| C2×#11745266 | 2 |
| #14271730 | 2 |
| #14271644 | 2 |
| #14271384 | 2 |
| #14271377 | 2 |
| #14271362 | 2 |
| #14271357 | 2 |
| #14271189 | 2 |
| #14271162 | 2 |
| C2×C29×#102 | 2 |
| #3045 | 29 |