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×#11745311 | C2 | semidirect |
| 2. C2×#11745263 | C2 | semidirect |
| 3. #14271741 | C2 | semidirect |
| 4. #14271732 | C2 | semidirect |
| 5. #14271415 | C2 | semidirect |
| 6. #14271412 | C2 | semidirect |
| 7. #14271398 | C2 | semidirect |
| 8. #14271395 | C2 | semidirect |
| 9. #14271206 | C2 | semidirect |
| 10. C2×#11745169 | C2 | semidirect |
| 11. C29×#416 | C2 | semidirect |
| 18. #11745308 | C22 | semidirect |
| 21. #11745300 | C22 | semidirect |
| 28. C2×#90772 | C22 | semidirect |
| 29. C2×C8×D29 | C22 | semidirect |
| 35. C29×#103 | C22 | semidirect |
| 36. C29×#103 | C22 | semidirect |
| 37. C29×#102 | C22 | semidirect |
| 38. C29×#102 | C22 | semidirect |
| 41. #11745156 | C22 | semidirect |
| 42. #11745155 | C22 | semidirect |
| 81. #90777 | D4 | semidirect |
| 154. #416 | D29 | semidirect |
| 188. #103 | C2×D29 | semidirect |
| 189. #103 | C2×D29 | semidirect |
| 192. #102 | C2×D29 | semidirect |
| 193. #102 | C2×D29 | semidirect |
| 194. C29 | #3062 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745311 | 2 |
| C2×#11745263 | 2 |
| #14271741 | 2 |
| #14271732 | 2 |
| #14271415 | 2 |
| #14271412 | 2 |
| #14271398 | 2 |
| #14271395 | 2 |
| #14271206 | 2 |
| C2×#11745169 | 2 |
| C29×#416 | 2 |
| #3062 | 29 |