Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 141 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×#11924527 | C2 | semidirect |
| 3. #14557896 | C2 | direct (N × H) |
| 4. C2×#11924458 | C2 | semidirect |
| 5. C2×#11924457 | C2 | semidirect |
| 6. C2×#11924456 | C2 | semidirect |
| 7. C2×#11924446 | C2 | semidirect |
| 8. C2×#102×C37 | C2 | semidirect |
| 16. #11924527 | C22 | semidirect |
| 21. #11924458 | C22 | semidirect |
| 22. #11924457 | C22 | semidirect |
| 23. #11924456 | C22 | semidirect |
| 24. #11924446 | C22 | semidirect |
| 28. #102×C37 | C22 | semidirect |
| 112. C2×C37 | #490 | semidirect |
| 123. C2×#102 | D37 | semidirect |
| 125. C37 | C2×#490 | semidirect |
| 144. #102 | C2×D37 | semidirect |
| 229. C2 | #14557896 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924532 | 2 |
| C2×#11924527 | 2 |
| #14557896 | 2 |
| C2×#11924458 | 2 |
| C2×#11924457 | 2 |
| C2×#11924456 | 2 |
| C2×#11924446 | 2 |
| C2×#102×C37 | 2 |
| C2×#490 | 37 |