Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#11924569 | C2 | semidirect |
| 2. C2×#11924556 | C2 | semidirect |
| 3. C22×#10596940 | C2 | semidirect |
| 4. #14558104 | C2 | semidirect |
| 5. #14558100 | C2 | semidirect |
| 6. #14557924 | C2 | semidirect |
| 7. #14557921 | C2 | semidirect |
| 8. #14557916 | C2 | semidirect |
| 9. #14557904 | C2 | semidirect |
| 10. #14557491 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C37 | C2 | semidirect |
| 16. C2×Dic148 | C22 | semidirect |
| 17. C2×#10596942 | C22 | semidirect |
| 18. C2×#10596930 | C22 | semidirect |
| 22. C2×#10596940 | C22 | semidirect |
| 23. C2×#10596941 | C22 | semidirect |
| 24. C2×#10596939 | C22 | semidirect |
| 26. #11924534 | C22 | semidirect |
| 29. #11924523 | C22 | semidirect |
| 35. #11924446 | C22 | semidirect |
| 36. C8×Dic37 | C22 | semidirect |
| 69. M16×C37 | D4 | semidirect |
| 83. C2×#64436 | D4 | semidirect |
| 150. C2×AGL(1,ℤ/8) | D37 | semidirect |
| 160. C37 | #3154 | semidirect |
| 226. M16 | C22⋊D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924569 | 2 |
| C2×#11924556 | 2 |
| C22×#10596940 | 2 |
| #14558104 | 2 |
| #14558100 | 2 |
| #14557924 | 2 |
| #14557921 | 2 |
| #14557916 | 2 |
| #14557904 | 2 |
| #14557491 | 2 |
| C2×AGL(1,ℤ/8)×C37 | 2 |
| #3154 | 37 |