Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
564 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
| 3. C2×#11924524 | C2 | semidirect |
| 4. C2×C4×D148 | C2 | semidirect |
| 5. #14557749 | C2 | direct (N × H) |
| 6. C2×#11924461 | C2 | semidirect |
| 7. C2×#11924458 | C2 | semidirect |
| 8. C2×C4⋊C8×C37 | C2 | semidirect |
| 14. C2×#10596930 | C22 | semidirect |
| 18. #11924524 | C22 | semidirect |
| 20. C4×D148 | C22 | semidirect |
| 25. #11924461 | C22 | semidirect |
| 26. #11924458 | C22 | semidirect |
| 30. C4⋊C8×C37 | C22 | semidirect |
| 118. C2×C37 | #463 | semidirect |
| 129. C2×C4⋊C8 | D37 | semidirect |
| 132. C37 | C2×#463 | semidirect |
| 152. C4⋊C8 | C2×D37 | semidirect |
| 243. C2 | #14557749 | 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 |
| C22×D296 | 2 |
| C2×#11924524 | 2 |
| C2×C4×D148 | 2 |
| #14557749 | 2 |
| C2×#11924461 | 2 |
| C2×#11924458 | 2 |
| C2×C4⋊C8×C37 | 2 |
| C2×#463 | 37 |