Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
364 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 129 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. #14558090 | C2 | semidirect |
| 3. #14557942 | C2 | semidirect |
| 4. #14557927 | C2 | semidirect |
| 5. #14557902 | C2 | semidirect |
| 6. #14557893 | C2 | semidirect |
| 7. #14557791 | C2 | semidirect |
| 9. C4×Dic148 | C2 | semidirect |
| 10. C4×#10596930 | C2 | semidirect |
| 11. C4×M16×C37 | C2 | semidirect |
| 140. C4×M16 | D37 | semidirect |
| 141. C37 | #3172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558090 | 2 |
| #14558067 | 2 |
| #14557942 | 2 |
| #14557927 | 2 |
| #14557902 | 2 |
| #14557893 | 2 |
| #14557791 | 2 |
| #14557779 | 2 |
| C4×Dic148 | 2 |
| C4×#10596930 | 2 |
| C4×M16×C37 | 2 |
| #3172 | 37 |