Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 125 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. #14558067 | C2 | semidirect |
| 2. #14557935 | C2 | semidirect |
| 3. #14557917 | C2 | semidirect |
| 4. #14557888 | C2 | semidirect |
| 5. #14557791 | C2 | semidirect |
| 7. #14557779 | C2 | semidirect |
| 8. #14557646 | C2 | semidirect |
| 9. #14557641 | C2 | semidirect |
| 10. #14557635 | C2 | semidirect |
| 11. C4×M16×C37 | C2 | semidirect |
| 120. C4×M16 | D37 | semidirect |
| 121. C37 | #3183 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558067 | 2 |
| #14557935 | 2 |
| #14557917 | 2 |
| #14557888 | 2 |
| #14557791 | 2 |
| #14557786 | 2 |
| #14557779 | 2 |
| #14557646 | 2 |
| #14557641 | 2 |
| #14557635 | 2 |
| C4×M16×C37 | 2 |
| #3183 | 37 |