Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
994 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 157 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. C23×D116 | C2 | semidirect |
| 2. C2×#11745270 | C2 | semidirect |
| 3. #14271674 | C2 | semidirect |
| 4. #14271316 | C2 | semidirect |
| 5. #14271299 | C2 | semidirect |
| 6. #14271169 | C2 | semidirect |
| 7. C29×#407 | C2 | semidirect |
| 10. C2×#90805 | C22 | semidirect |
| 16. C2×M16×C29 | C22 | semidirect |
| 18. #11745292 | C22 | semidirect |
| 21. #11745288 | C22 | semidirect |
| 22. #11745286 | C22 | semidirect |
| 24. C2×D232 | C22 | semidirect |
| 25. C2×#90773 | C22 | semidirect |
| 26. C29×C22⋊C8 | C22 | semidirect |
| 27. #11745169 | C22 | semidirect |
| 47. C2×D116 | D4 | semidirect |
| 49. C2×D116 | C23 | semidirect |
| 51. C2×Dic58 | C23 | semidirect |
| 53. C2×C8×C29 | C23 | semidirect |
| 57. C4⋊Dic29 | C23 | semidirect |
| 99. C22×C29 | AGL(1,ℤ/8) | semidirect |
| 118. #407 | D29 | semidirect |
| 136. C2×M16 | C2×D29 | semidirect |
| 144. C22⋊C8 | C2×D29 | semidirect |
| 145. C29 | #3003 | semidirect |
| 173. C2×C8 | C22×D29 | semidirect |
| 222. C22 | #11745270 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D116 | 2 |
| C2×#11745270 | 2 |
| #14271674 | 2 |
| #14271316 | 2 |
| #14271299 | 2 |
| #14271169 | 2 |
| C29×#407 | 2 |
| #3003 | 29 |