Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
500 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 127 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×#11745274 | C2 | semidirect |
| 2. C2×M16×D29 | C2 | semidirect |
| 3. #14271673 | C2 | semidirect |
| 4. #14271422 | C2 | semidirect |
| 5. #14271421 | C2 | semidirect |
| 6. #14271413 | C2 | semidirect |
| 7. #14271408 | C2 | semidirect |
| 8. #14271407 | C2 | semidirect |
| 9. #14271198 | C2 | semidirect |
| 10. #14271156 | C2 | semidirect |
| 11. C29×#469 | C2 | semidirect |
| 14. C2×D8×C29 | C22 | semidirect |
| 20. C2×#90783 | C22 | semidirect |
| 25. C2×Dic116 | C22 | semidirect |
| 34. C29×#106 | C22 | semidirect |
| 35. C29×#102 | C22 | semidirect |
| 36. #11745180 | C22 | semidirect |
| 37. #11745165 | C22 | semidirect |
| 38. #11745164 | C22 | semidirect |
| 39. #11745158 | C22 | semidirect |
| 40. #11745155 | C22 | semidirect |
| 80. C8×D29 | D4 | semidirect |
| 141. #469 | D29 | semidirect |
| 157. C2×D8 | C2×D29 | semidirect |
| 176. #106 | C2×D29 | semidirect |
| 180. #102 | C2×D29 | semidirect |
| 181. C29 | #3054 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745274 | 2 |
| C2×M16×D29 | 2 |
| #14271673 | 2 |
| #14271422 | 2 |
| #14271421 | 2 |
| #14271413 | 2 |
| #14271408 | 2 |
| #14271407 | 2 |
| #14271198 | 2 |
| #14271156 | 2 |
| C29×#469 | 2 |
| #3054 | 29 |