Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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. #14558156 | C2 | semidirect |
| 2. #14557937 | C2 | semidirect |
| 3. #14557918 | C2 | semidirect |
| 4. #14557894 | C2 | semidirect |
| 5. #14557781 | C2 | semidirect |
| 7. #14557636 | C2 | semidirect |
| 8. Q16×Dic37 | C2 | semidirect |
| 9. #14557615 | C2 | semidirect |
| 10. #14557488 | C2 | semidirect |
| 11. C37×#467 | C2 | semidirect |
| 123. #467 | 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 |
|---|---|
| #14558156 | 2 |
| #14557937 | 2 |
| #14557918 | 2 |
| #14557894 | 2 |
| #14557781 | 2 |
| #14557769 | 2 |
| #14557636 | 2 |
| Q16×Dic37 | 2 |
| #14557615 | 2 |
| #14557488 | 2 |
| C37×#467 | 2 |
| #3175 | 37 |