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. #14558152 | C2 | semidirect |
| 2. #14557938 | C2 | semidirect |
| 3. #14557892 | C2 | semidirect |
| 4. #14557776 | C2 | semidirect |
| 5. #14557771 | C2 | semidirect |
| 7. #14557634 | C2 | semidirect |
| 8. Q16×Dic37 | C2 | semidirect |
| 9. D8×Dic37 | C2 | semidirect |
| 10. #14557487 | C2 | semidirect |
| 11. C37×#495 | C2 | semidirect |
| 120. #495 | D37 | semidirect |
| 129. C37 | #3175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558152 | 2 |
| #14557938 | 2 |
| #14557892 | 2 |
| #14557776 | 2 |
| #14557771 | 2 |
| #14557766 | 2 |
| #14557634 | 2 |
| Q16×Dic37 | 2 |
| D8×Dic37 | 2 |
| #14557487 | 2 |
| C37×#495 | 2 |
| #3175 | 37 |