Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 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. C2×#11745270 | C2 | semidirect |
| 2. C2×#11745269 | C2 | semidirect |
| 3. #14271744 | C2 | semidirect |
| 4. #14271732 | C2 | semidirect |
| 5. #14271417 | C2 | semidirect |
| 6. #14271410 | C2 | semidirect |
| 7. #14271400 | C2 | semidirect |
| 8. #14271393 | C2 | semidirect |
| 9. #14271157 | C2 | semidirect |
| 10. C2×#11745157 | C2 | semidirect |
| 11. C29×#428 | C2 | semidirect |
| 24. C2×#90772 | C22 | semidirect |
| 25. C2×C8×D29 | C22 | semidirect |
| 27. #11745259 | C22 | semidirect |
| 31. #11745257 | C22 | semidirect |
| 35. C29×#107 | C22 | semidirect |
| 36. C29×#106 | C22 | semidirect |
| 37. #11745158 | C22 | semidirect |
| 38. #11745158 | C22 | semidirect |
| 41. #11745157 | C22 | semidirect |
| 42. #11745157 | C22 | semidirect |
| 65. M16×C29 | D4 | semidirect |
| 153. #428 | D29 | semidirect |
| 186. #107 | C2×D29 | semidirect |
| 187. #106 | C2×D29 | semidirect |
| 194. C29 | #3062 | semidirect |
| 220. M16 | D116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745270 | 2 |
| C2×#11745269 | 2 |
| #14271744 | 2 |
| #14271732 | 2 |
| #14271417 | 2 |
| #14271410 | 2 |
| #14271400 | 2 |
| #14271393 | 2 |
| #14271157 | 2 |
| C2×#11745157 | 2 |
| C29×#428 | 2 |
| #3062 | 29 |