Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 125 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. #14271977 | C2 | semidirect |
| 2. #14271974 | C2 | semidirect |
| 3. #14271546 | C2 | semidirect |
| 4. #14271438 | C2 | semidirect |
| 5. #14271430 | C2 | semidirect |
| 6. #14271424 | C2 | semidirect |
| 7. #14271341 | C2 | semidirect |
| 8. #14271334 | C2 | semidirect |
| 9. #14271280 | C2 | semidirect |
| 10. #14271278 | C2 | semidirect |
| 11. C29×#576 | C2 | semidirect |
| 13. #11745365 | C22 | semidirect |
| 23. #11745313 | C22 | semidirect |
| 26. #11745310 | C22 | semidirect |
| 27. #11745298 | C22 | semidirect |
| 29. C2×#90783 | C22 | semidirect |
| 31. #11745294 | C22 | semidirect |
| 35. C2×Dic116 | C22 | semidirect |
| 36. #11745263 | C22 | semidirect |
| 38. #11745185 | C22 | semidirect |
| 39. #11745181 | C22 | semidirect |
| 40. #11745173 | C22 | semidirect |
| 41. #11745172 | C22 | semidirect |
| 42. #11745170 | C22 | semidirect |
| 43. #11745167 | C22 | semidirect |
| 44. C8×Dic29 | C22 | semidirect |
| 146. #576 | D29 | semidirect |
| 194. C29 | #3290 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271977 | 2 |
| #14271974 | 2 |
| #14271546 | 2 |
| #14271438 | 2 |
| #14271430 | 2 |
| #14271424 | 2 |
| #14271341 | 2 |
| #14271334 | 2 |
| #14271280 | 2 |
| #14271278 | 2 |
| C29×#576 | 2 |
| #3290 | 29 |