Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
388 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 3. #14557884 | C2 | semidirect |
| 4. #14557869 | C2 | semidirect |
| 5. #14557829 | C2 | semidirect |
| 6. #14557774 | C2 | semidirect |
| 7. #14557744 | C2 | semidirect |
| 8. #14557691 | C2 | semidirect |
| 9. C4×Dic148 | C2 | semidirect |
| 10. C2×#11924461 | C2 | semidirect |
| 77. D4×C37 | Q16 | semidirect |
| 134. C37 | #3299 | semidirect |
| 208. D4 | Dic148 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558240 | 2 |
| D4×Dic74 | 2 |
| #14557884 | 2 |
| #14557869 | 2 |
| #14557829 | 2 |
| #14557774 | 2 |
| #14557744 | 2 |
| #14557691 | 2 |
| C4×Dic148 | 2 |
| C2×#11924461 | 2 |
| C8×D4×C37 | 2 |
| #3299 | 37 |