Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
462 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 462 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 |
|---|---|---|
| 2. #117×D29 | C2 | semidirect |
| 3. #14271490 | C2 | semidirect |
| 4. #14271489 | C2 | semidirect |
| 5. #14271483 | C2 | semidirect |
| 6. #14271478 | C2 | semidirect |
| 7. #14271203 | C2 | semidirect |
| 8. #14271169 | C2 | semidirect |
| 9. #14271167 | C2 | semidirect |
| 10. #14271126 | C2 | semidirect |
| 11. C29×#428 | C2 | semidirect |
| 25. #11745254 | C22 | semidirect |
| 26. #11745254 | C22 | semidirect |
| 27. C4⋊C4×D29 | C22 | semidirect |
| 28. C4⋊C4×D29 | C22 | semidirect |
| 33. C29×#107 | C22 | semidirect |
| 34. C29×#106 | C22 | semidirect |
| 35. #11745169 | C22 | semidirect |
| 36. #11745169 | C22 | semidirect |
| 37. #11745168 | C22 | semidirect |
| 38. #11745168 | C22 | semidirect |
| 39. #11745157 | C22 | semidirect |
| 40. #11745157 | C22 | semidirect |
| 41. #11745156 | C22 | semidirect |
| 42. #11745155 | C22 | semidirect |
| 156. #428 | D29 | semidirect |
| 189. #107 | C2×D29 | semidirect |
| 191. #106 | C2×D29 | semidirect |
| 198. C29 | #3094 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745257 | 2 |
| #117×D29 | 2 |
| #14271490 | 2 |
| #14271489 | 2 |
| #14271483 | 2 |
| #14271478 | 2 |
| #14271203 | 2 |
| #14271169 | 2 |
| #14271167 | 2 |
| #14271126 | 2 |
| C29×#428 | 2 |
| #3094 | 29 |