Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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. #14558146 | C2 | semidirect |
| 3. #14557906 | C2 | semidirect |
| 4. #14557903 | C2 | semidirect |
| 5. #14557899 | C2 | semidirect |
| 6. #14557780 | C2 | semidirect |
| 7. #14557763 | C2 | semidirect |
| 8. #14557632 | C2 | semidirect |
| 9. #14557620 | C2 | semidirect |
| 10. #14557487 | C2 | semidirect |
| 11. C37×#499 | C2 | semidirect |
| 111. #499 | D37 | semidirect |
| 120. C37 | #3174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558146 | 2 |
| #14558139 | 2 |
| #14557906 | 2 |
| #14557903 | 2 |
| #14557899 | 2 |
| #14557780 | 2 |
| #14557763 | 2 |
| #14557632 | 2 |
| #14557620 | 2 |
| #14557487 | 2 |
| C37×#499 | 2 |
| #3174 | 37 |