Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #14558064 | C2 | semidirect |
| 2. #14557934 | C2 | semidirect |
| 3. #14557916 | C2 | semidirect |
| 4. #14557886 | C2 | semidirect |
| 5. #14557774 | C2 | semidirect |
| 6. #14557760 | C2 | semidirect |
| 7. #14557627 | C2 | semidirect |
| 8. #14557624 | C2 | semidirect |
| 9. D8×Dic37 | C2 | semidirect |
| 10. C2×C8×Dic37 | C2 | semidirect |
| 130. C37 | #3168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558064 | 2 |
| #14557934 | 2 |
| #14557916 | 2 |
| #14557886 | 2 |
| #14557774 | 2 |
| #14557760 | 2 |
| #14557627 | 2 |
| #14557624 | 2 |
| D8×Dic37 | 2 |
| C2×C8×Dic37 | 2 |
| C37×#466 | 2 |
| #3168 | 37 |