Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
354 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 354 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 |
|---|---|---|
| 2. #14558243 | C2 | semidirect |
| 3. #14557938 | C2 | semidirect |
| 4. #14557873 | C2 | semidirect |
| 5. #14557845 | C2 | semidirect |
| 6. #14557828 | C2 | semidirect |
| 7. #14557823 | C2 | semidirect |
| 8. #14557776 | C2 | semidirect |
| 9. #14557612 | C2 | semidirect |
| 10. #14557572 | C2 | semidirect |
| 11. C4×SD16×C37 | C2 | semidirect |
| 130. C4×SD16 | D37 | semidirect |
| 133. C37 | #3357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558248 | 2 |
| #14558243 | 2 |
| #14557938 | 2 |
| #14557873 | 2 |
| #14557845 | 2 |
| #14557828 | 2 |
| #14557823 | 2 |
| #14557776 | 2 |
| #14557612 | 2 |
| #14557572 | 2 |
| C4×SD16×C37 | 2 |
| #3357 | 37 |