Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
426 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 426 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. #14558203 | C2 | semidirect |
| 2. D4×Dic74 | C2 | semidirect |
| 3. #14557879 | C2 | semidirect |
| 4. #14557878 | C2 | semidirect |
| 5. #14557814 | C2 | semidirect |
| 6. #14557811 | C2 | semidirect |
| 7. #14557726 | C2 | semidirect |
| 8. #14557657 | C2 | semidirect |
| 9. D8×Dic37 | C2 | semidirect |
| 10. C4×#10596939 | C2 | semidirect |
| 11. C37×#459 | C2 | semidirect |
| 83. D4×C37 | #41 | semidirect |
| 102. Dic74 | D8 | semidirect |
| 139. #459 | D37 | semidirect |
| 143. C37 | #3358 | semidirect |
| 222. D4 | #10596964 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558203 | 2 |
| D4×Dic74 | 2 |
| #14557879 | 2 |
| #14557878 | 2 |
| #14557814 | 2 |
| #14557811 | 2 |
| #14557726 | 2 |
| #14557657 | 2 |
| D8×Dic37 | 2 |
| C4×#10596939 | 2 |
| C37×#459 | 2 |
| #3358 | 37 |