Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
342 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 342 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 |
|---|---|---|
| 3. #14557931 | C2 | semidirect |
| 4. #14557872 | C2 | semidirect |
| 5. #14557862 | C2 | semidirect |
| 6. #14557828 | C2 | semidirect |
| 7. #14557818 | C2 | semidirect |
| 8. #14557788 | C2 | semidirect |
| 10. #14557574 | C2 | semidirect |
| 11. C4×Q16×C37 | C2 | semidirect |
| 125. C4×Q16 | D37 | semidirect |
| 128. C37 | #3356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558256 | 2 |
| #14558243 | 2 |
| #14557931 | 2 |
| #14557872 | 2 |
| #14557862 | 2 |
| #14557828 | 2 |
| #14557818 | 2 |
| #14557788 | 2 |
| #14557612 | 2 |
| #14557574 | 2 |
| C4×Q16×C37 | 2 |
| #3356 | 37 |