Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 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. #14558086 | C2 | semidirect |
| 3. #14557900 | C2 | semidirect |
| 4. #14557896 | C2 | semidirect |
| 5. #14557894 | C2 | semidirect |
| 6. #14557891 | C2 | semidirect |
| 7. #14557530 | C2 | semidirect |
| 8. #14557529 | C2 | semidirect |
| 9. #14557527 | C2 | semidirect |
| 10. C2×#11924446 | C2 | semidirect |
| 11. C37×#416 | C2 | semidirect |
| 135. #416 | D37 | semidirect |
| 137. C37 | #3135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558086 | 2 |
| #14558079 | 2 |
| #14557900 | 2 |
| #14557896 | 2 |
| #14557894 | 2 |
| #14557891 | 2 |
| #14557530 | 2 |
| #14557529 | 2 |
| #14557527 | 2 |
| C2×#11924446 | 2 |
| C37×#416 | 2 |
| #3135 | 37 |