Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
544 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 197 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. C2×Q8×Dic37 | C2 | semidirect |
| 4. #14557636 | C2 | direct (N × H) |
| 5. C2×#11924469 | C2 | semidirect |
| 7. C2×#11924446 | C2 | semidirect |
| 8. C2×#103×C37 | C2 | semidirect |
| 11. C2×#10596941 | C4 | semidirect |
| 15. Q8×Dic37 | C22 | semidirect |
| 23. #11924469 | C22 | semidirect |
| 25. #11924446 | C22 | semidirect |
| 29. #103×C37 | C22 | semidirect |
| 33. C2×Q8×C37 | C2×C4 | semidirect |
| 51. #10596941 | C2×C4 | semidirect |
| 59. C2×#64436 | C2×C4 | semidirect |
| 68. Q8×C37 | C22×C4 | semidirect |
| 88. #64436 | C22×C4 | semidirect |
| 106. C2×C37 | #440 | semidirect |
| 116. C2×#103 | D37 | semidirect |
| 119. C37 | C2×#440 | semidirect |
| 138. #103 | C2×D37 | semidirect |
| 144. C2×Q8 | C4×D37 | semidirect |
| 179. Q8 | C2×C4×D37 | semidirect |
| 217. C2 | #14557636 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596941 | 2 |
| C2×Q8×Dic37 | 2 |
| C2×#11924498 | 2 |
| #14557636 | 2 |
| C2×#11924469 | 2 |
| C2×#11924458 | 2 |
| C2×#11924446 | 2 |
| C2×#103×C37 | 2 |
| C2×#440 | 37 |