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. #14558069 | C2 | semidirect |
| 2. #14557934 | C2 | semidirect |
| 3. #14557918 | C2 | semidirect |
| 4. #14557889 | C2 | semidirect |
| 6. #14557764 | C2 | semidirect |
| 7. Q16×Dic37 | C2 | semidirect |
| 8. #14557618 | C2 | semidirect |
| 9. #14557615 | C2 | semidirect |
| 10. C2×C8×Dic37 | C2 | semidirect |
| 11. C37×#467 | C2 | semidirect |
| 123. #467 | D37 | semidirect |
| 130. C37 | #3168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558069 | 2 |
| #14557934 | 2 |
| #14557918 | 2 |
| #14557889 | 2 |
| #14557769 | 2 |
| #14557764 | 2 |
| Q16×Dic37 | 2 |
| #14557618 | 2 |
| #14557615 | 2 |
| C2×C8×Dic37 | 2 |
| C37×#467 | 2 |
| #3168 | 37 |