Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
408 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 408 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. #14558248 | C2 | semidirect |
| 2. #14557879 | C2 | semidirect |
| 3. #14557854 | C2 | semidirect |
| 4. #14557828 | C2 | semidirect |
| 5. #14557767 | C2 | semidirect |
| 6. #14557725 | C2 | semidirect |
| 7. #14557678 | C2 | semidirect |
| 8. C4×#10596941 | C2 | semidirect |
| 9. D4×#64436 | C2 | semidirect |
| 10. #14557529 | C2 | semidirect |
| 11. C37×#550 | C2 | semidirect |
| 134. #550 | D37 | semidirect |
| 144. C37 | #3305 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558248 | 2 |
| #14557879 | 2 |
| #14557854 | 2 |
| #14557828 | 2 |
| #14557767 | 2 |
| #14557725 | 2 |
| #14557678 | 2 |
| C4×#10596941 | 2 |
| D4×#64436 | 2 |
| #14557529 | 2 |
| C37×#550 | 2 |
| #3305 | 37 |