Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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. #14558233 | C2 | semidirect |
| 2. #14557935 | C2 | semidirect |
| 3. #14557855 | C2 | semidirect |
| 4. #14557845 | C2 | semidirect |
| 5. #14557833 | C2 | semidirect |
| 6. #14557783 | C2 | semidirect |
| 7. #14557612 | C2 | semidirect |
| 8. #14557574 | C2 | semidirect |
| 9. C4×D8×C37 | C2 | semidirect |
| 109. C4×D8 | D37 | semidirect |
| 112. C37 | #3355 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558233 | 2 |
| #14557935 | 2 |
| #14557855 | 2 |
| #14557845 | 2 |
| #14557833 | 2 |
| #14557783 | 2 |
| #14557612 | 2 |
| #14557574 | 2 |
| C4×D8×C37 | 2 |
| #3355 | 37 |