Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#90773 | C2 | semidirect |
| 2. C2×#11745263 | C2 | semidirect |
| 3. #14271739 | C2 | semidirect |
| 5. #14271410 | C2 | semidirect |
| 6. #14271393 | C2 | semidirect |
| 7. #14271171 | C2 | semidirect |
| 8. #14271167 | C2 | semidirect |
| 9. C29×#427 | C2 | semidirect |
| 21. C2×#90772 | C22 | semidirect |
| 22. C2×C8×D29 | C22 | semidirect |
| 23. #11745259 | C22 | semidirect |
| 31. C29×#107 | C22 | semidirect |
| 32. C29×#106 | C22 | semidirect |
| 33. #11745158 | C22 | semidirect |
| 53. C2×C8×C29 | D4 | semidirect |
| 122. #427 | D29 | semidirect |
| 151. #107 | C2×D29 | semidirect |
| 152. #106 | C2×D29 | semidirect |
| 155. C29 | #3057 | semidirect |
| 180. C2×C8 | D116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90773 | 2 |
| C2×#11745263 | 2 |
| #14271739 | 2 |
| #14271732 | 2 |
| #14271410 | 2 |
| #14271393 | 2 |
| #14271171 | 2 |
| #14271167 | 2 |
| C29×#427 | 2 |
| #3057 | 29 |