Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #14558256 | C2 | semidirect |
| 3. #14557880 | C2 | semidirect |
| 4. #14557860 | C2 | semidirect |
| 5. #14557818 | C2 | semidirect |
| 6. #14557765 | C2 | semidirect |
| 7. #14557733 | C2 | semidirect |
| 8. #14557694 | C2 | semidirect |
| 9. C8×D148 | C2 | semidirect |
| 10. #14557528 | C2 | semidirect |
| 11. C4×Q16×C37 | C2 | semidirect |
| 136. C4×Q16 | D37 | semidirect |
| 139. C37 | #3304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558256 | 2 |
| #14558205 | 2 |
| #14557880 | 2 |
| #14557860 | 2 |
| #14557818 | 2 |
| #14557765 | 2 |
| #14557733 | 2 |
| #14557694 | 2 |
| C8×D148 | 2 |
| #14557528 | 2 |
| C4×Q16×C37 | 2 |
| #3304 | 37 |