Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
544 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#10596930 | C2 | semidirect |
| 2. C2×#11924515 | C2 | semidirect |
| 4. #14557779 | C2 | direct (N × H) |
| 5. C2×#11924470 | C2 | semidirect |
| 6. C2×#11924461 | C2 | semidirect |
| 7. C2×#11924458 | C2 | semidirect |
| 8. C22×M16×C37 | C2 | semidirect |
| 13. C2×#10596930 | C22 | semidirect |
| 15. #11924515 | C22 | semidirect |
| 23. #11924470 | C22 | semidirect |
| 24. #11924461 | C22 | semidirect |
| 25. #11924458 | C22 | semidirect |
| 28. C2×M16×C37 | C22 | semidirect |
| 54. C2×C8×C37 | D4 | semidirect |
| 97. C8×C37 | C2×D4 | semidirect |
| 119. C2×C37 | #468 | semidirect |
| 125. C22×M16 | D37 | semidirect |
| 132. C37 | C2×#468 | semidirect |
| 140. C2×M16 | C2×D37 | semidirect |
| 179. C2×C8 | C22⋊D37 | semidirect |
| 221. C8 | C2×C22⋊D37 | semidirect |
| 243. C2 | #14557779 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596930 | 2 |
| C2×#11924515 | 2 |
| C2×#11924510 | 2 |
| #14557779 | 2 |
| C2×#11924470 | 2 |
| C2×#11924461 | 2 |
| C2×#11924458 | 2 |
| C22×M16×C37 | 2 |
| C2×#468 | 37 |