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. #14558204 | C2 | semidirect |
| 2. D4×Dic74 | C2 | semidirect |
| 3. #14557880 | C2 | semidirect |
| 4. #14557878 | C2 | semidirect |
| 5. #14557813 | C2 | semidirect |
| 6. #14557812 | C2 | semidirect |
| 7. #14557728 | C2 | semidirect |
| 8. #14557726 | C2 | semidirect |
| 9. C8×Dic74 | C2 | semidirect |
| 10. #14557613 | C2 | semidirect |
| 11. C4×D8×C37 | C2 | semidirect |
| 81. D4×C37 | #41 | semidirect |
| 102. Dic74 | D8 | semidirect |
| 142. C4×D8 | D37 | semidirect |
| 143. C37 | #3358 | semidirect |
| 222. D4 | #10596962 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558204 | 2 |
| D4×Dic74 | 2 |
| #14557880 | 2 |
| #14557878 | 2 |
| #14557813 | 2 |
| #14557812 | 2 |
| #14557728 | 2 |
| #14557726 | 2 |
| C8×Dic74 | 2 |
| #14557613 | 2 |
| C4×D8×C37 | 2 |
| #3358 | 37 |