Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
396 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 2. #14557881 | C2 | semidirect |
| 3. #14557857 | C2 | semidirect |
| 4. #14557815 | C2 | semidirect |
| 5. #14557764 | C2 | semidirect |
| 6. #14557733 | C2 | semidirect |
| 7. #14557693 | C2 | semidirect |
| 8. C4×#10596942 | C2 | semidirect |
| 9. D4×#64436 | C2 | semidirect |
| 10. #14557527 | C2 | semidirect |
| 11. C37×#556 | C2 | semidirect |
| 128. #556 | D37 | semidirect |
| 139. C37 | #3304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558204 | 2 |
| #14557881 | 2 |
| #14557857 | 2 |
| #14557815 | 2 |
| #14557764 | 2 |
| #14557733 | 2 |
| #14557693 | 2 |
| C4×#10596942 | 2 |
| D4×#64436 | 2 |
| #14557527 | 2 |
| C37×#556 | 2 |
| #3304 | 37 |