Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
688 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 173 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. #14557433 | C2 | semidirect |
| 3. #14557427 | C2 | semidirect |
| 4. #14557421 | C2 | semidirect |
| 5. #14557409 | C2 | semidirect |
| 6. #14557389 | C2 | semidirect |
| 7. C37×#379 | C2 | semidirect |
| 9. C22×C4×D37 | C22 | semidirect |
| 10. #11924505 | C4 | semidirect |
| 11. C2×#10596936 | C22 | semidirect |
| 15. C2×#10596938 | C22 | semidirect |
| 16. C2×C4×Dic37 | C22 | semidirect |
| 17. #11924443 | C22 | semidirect |
| 18. #11924443 | C22 | semidirect |
| 24. C24×C37 | C2×C4 | semidirect |
| 40. C22⋊Dic37 | C2×C4 | semidirect |
| 102. #379 | D37 | semidirect |
| 103. C37 | #2375 | semidirect |
| 121. C24 | C4×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924505 | 2 |
| #14557433 | 2 |
| #14557427 | 2 |
| #14557421 | 2 |
| #14557409 | 2 |
| #14557389 | 2 |
| C37×#379 | 2 |
| #2375 | 37 |