Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
426 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 426 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 |
|---|---|---|
| 1. #14558203 | C2 | semidirect |
| 2. #14558198 | C2 | semidirect |
| 3. #14557878 | C2 | semidirect |
| 4. #14557811 | C2 | semidirect |
| 5. #14557810 | C2 | semidirect |
| 6. #14557727 | C2 | semidirect |
| 7. #14557725 | C2 | semidirect |
| 8. C8×Dic74 | C2 | semidirect |
| 9. C4×D296 | C2 | semidirect |
| 10. #14557613 | C2 | semidirect |
| 11. C37×#486 | C2 | semidirect |
| 97. D148 | #41 | semidirect |
| 102. Dic74 | D8 | semidirect |
| 135. #486 | D37 | semidirect |
| 143. C37 | #3358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558203 | 2 |
| #14558198 | 2 |
| #14557878 | 2 |
| #14557811 | 2 |
| #14557810 | 2 |
| #14557727 | 2 |
| #14557725 | 2 |
| C8×Dic74 | 2 |
| C4×D296 | 2 |
| #14557613 | 2 |
| C37×#486 | 2 |
| #3358 | 37 |