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. #14557436 | C2 | semidirect |
| 3. #14557433 | C2 | semidirect |
| 4. #14557427 | C2 | semidirect |
| 5. #14557425 | C2 | semidirect |
| 6. #14557422 | C2 | semidirect |
| 7. #14557412 | C2 | semidirect |
| 8. #14557388 | C2 | semidirect |
| 9. C37×#386 | C2 | semidirect |
| 12. #11924504 | C4 | semidirect |
| 13. C2×C4⋊Dic37 | C22 | semidirect |
| 14. C2×#10596936 | C22 | semidirect |
| 17. C2×C22⋊Dic37 | C22 | semidirect |
| 23. C2×C4×Dic37 | C22 | semidirect |
| 24. C2×C4×Dic37 | C22 | semidirect |
| 25. #11924443 | C22 | semidirect |
| 26. #11924443 | C22 | semidirect |
| 28. C23×C4×C37 | C22 | semidirect |
| 30. C2×C22⋊C4×C37 | C22 | semidirect |
| 31. #95×C37 | C22 | semidirect |
| 38. C23×D37 | C2×C4 | semidirect |
| 58. C22⋊Dic37 | C2×C4 | semidirect |
| 63. #10596938 | C2×C4 | semidirect |
| 157. #386 | D37 | semidirect |
| 159. C37 | #2375 | semidirect |
| 163. C23×C4 | C2×D37 | semidirect |
| 176. C2×C22⋊C4 | C2×D37 | semidirect |
| 181. #95 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924504 | 2 |
| #14557436 | 2 |
| #14557433 | 2 |
| #14557427 | 2 |
| #14557425 | 2 |
| #14557422 | 2 |
| #14557412 | 2 |
| #14557388 | 2 |
| C37×#386 | 2 |
| #2375 | 37 |