Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
394 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 394 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. #14271775 | C2 | semidirect |
| 2. #14271504 | C2 | semidirect |
| 3. #14271463 | C2 | semidirect |
| 4. #14271368 | C2 | semidirect |
| 6. #14271263 | C2 | semidirect |
| 7. C4×#90783 | C2 | semidirect |
| 8. #14271224 | C2 | semidirect |
| 22. #11745232 | C22 | semidirect |
| 23. #11745231 | C22 | semidirect |
| 24. C4×Dic58 | C22 | semidirect |
| 28. #11745158 | C22 | semidirect |
| 29. #11745158 | C22 | semidirect |
| 30. #11745156 | C22 | semidirect |
| 31. #11745155 | C22 | semidirect |
| 32. C4⋊#6597 | C22 | semidirect |
| 33. #11745151 | C22 | semidirect |
| 34. C4×#6597 | C22 | semidirect |
| 137. C29 | #3123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271775 | 2 |
| #14271504 | 2 |
| #14271463 | 2 |
| #14271368 | 2 |
| #14271314 | 2 |
| #14271263 | 2 |
| C4×#90783 | 2 |
| #14271224 | 2 |
| C29×#518 | 2 |
| #3123 | 29 |