Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
1540 conjugacy classes of subgroups; only the 805 normal subgroups are shown.
This group has 1540 conjugacy classes of subgroups — too many to draw. Only its 805 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. #14558015 | C2 | semidirect |
| 3. #14558011 | C2 | semidirect |
| 4. #14558007 | C2 | semidirect |
| 5. C4×#10596966 | C2 | semidirect |
| 6. #117×D37 | C2 | semidirect |
| 7. C37×#519 | C2 | semidirect |
| 8. C2×#10596966 | C4 | semidirect |
| 13. Q8×Dic37 | C22 | semidirect |
| 14. C4×D148 | C22 | semidirect |
| 15. #11924498 | C22 | semidirect |
| 17. #11924494 | C22 | semidirect |
| 18. #11924493 | C22 | semidirect |
| 20. C4⋊C4×D37 | C22 | semidirect |
| 22. C42×D37 | C22 | semidirect |
| 24. C4×Q8×C37 | C22 | semidirect |
| 27. C2×Q8×C37 | C2×C4 | semidirect |
| 31. #10596966 | C2×C4 | semidirect |
| 32. #10596966 | C2×C4 | semidirect |
| 33. C2×D148 | C2×C4 | semidirect |
| 35. C2×C4×D37 | C2×C4 | semidirect |
| 83. #519 | D37 | semidirect |
| 87. C37 | #3428 | semidirect |
| 95. C4×Q8 | C2×D37 | semidirect |
| 109. C2×Q8 | C4×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596966 | 2 |
| #14558015 | 2 |
| #14558011 | 2 |
| #14558007 | 2 |
| C4×#10596966 | 2 |
| #117×D37 | 2 |
| C37×#519 | 2 |
| #3428 | 37 |