Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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. #14558155 | C2 | semidirect |
| 2. #14557937 | C2 | semidirect |
| 3. #14557918 | C2 | semidirect |
| 4. #14557894 | C2 | semidirect |
| 5. #14557782 | C2 | semidirect |
| 6. #14557771 | C2 | semidirect |
| 8. #14557631 | C2 | semidirect |
| 9. C4×D296 | C2 | semidirect |
| 10. #14557487 | C2 | semidirect |
| 11. C4×Q16×C37 | C2 | semidirect |
| 126. C4×Q16 | D37 | semidirect |
| 129. C37 | #3175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558155 | 2 |
| #14557937 | 2 |
| #14557918 | 2 |
| #14557894 | 2 |
| #14557782 | 2 |
| #14557771 | 2 |
| #14557770 | 2 |
| #14557631 | 2 |
| C4×D296 | 2 |
| #14557487 | 2 |
| C4×Q16×C37 | 2 |
| #3175 | 37 |