Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
458 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 217 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. #14558300 | C2 | semidirect |
| 2. #14557655 | C2 | semidirect |
| 3. #14557650 | C2 | semidirect |
| 4. #14557582 | C2 | semidirect |
| 5. C2×#11924463 | C2 | semidirect |
| 6. M16×Dic37 | C2 | semidirect |
| 9. #11924543 | C22 | semidirect |
| 14. #11924472 | C22 | semidirect |
| 15. #11924463 | C22 | semidirect |
| 16. #11924463 | C22 | semidirect |
| 17. #11924446 | C22 | semidirect |
| 18. C8×Dic37 | C22 | semidirect |
| 20. #137×C37 | C4 | semidirect |
| 21. AGL(1,ℤ/8)×C37 | C4 | semidirect |
| 34. Q16×C37 | C2×C4 | semidirect |
| 35. SD16×C37 | C2×C4 | semidirect |
| 36. D8×C37 | C2×C4 | semidirect |
| 93. C37 | #2956 | semidirect |
| 95. #137 | Dic37 | semidirect |
| 96. AGL(1,ℤ/8) | Dic37 | semidirect |
| 120. Q16 | C2×Dic37 | semidirect |
| 121. SD16 | C2×Dic37 | semidirect |
| 122. D8 | C2×Dic37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558300 | 2 |
| #14557655 | 2 |
| #14557650 | 2 |
| #14557582 | 2 |
| C2×#11924463 | 2 |
| M16×Dic37 | 2 |
| C37×#575 | 2 |
| #2956 | 37 |