Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
656 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 145 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×#11924560 | C2 | semidirect |
| 2. #14558081 | C2 | semidirect |
| 3. #127×D37 | C2 | semidirect |
| 4. #14557921 | C2 | semidirect |
| 5. #14557909 | C2 | semidirect |
| 6. #14557906 | C2 | semidirect |
| 7. #14557905 | C2 | semidirect |
| 8. C4×#10596929 | C2 | semidirect |
| 9. C37×#493 | C2 | semidirect |
| 14. C2×#10596930 | C22 | semidirect |
| 15. C2×#10596940 | C22 | semidirect |
| 16. C2×#10596939 | C22 | semidirect |
| 18. #11924536 | C22 | semidirect |
| 22. #11924523 | C22 | semidirect |
| 26. #11924446 | C22 | semidirect |
| 27. C4×#64436 | C22 | semidirect |
| 28. C2×D8×C37 | C22 | semidirect |
| 30. #127×C37 | C22 | semidirect |
| 31. C4×C8×C37 | C22 | semidirect |
| 60. #10596929 | D4 | semidirect |
| 85. C8×C37 | C2×D4 | semidirect |
| 86. #64436 | C2×D4 | semidirect |
| 97. C4×C37 | AGL(1,ℤ/8) | semidirect |
| 114. #493 | D37 | semidirect |
| 118. C37 | #3151 | semidirect |
| 126. C2×D8 | C2×D37 | semidirect |
| 133. #127 | C2×D37 | semidirect |
| 140. C4×C8 | C2×D37 | semidirect |
| 195. C8 | D4×D37 | semidirect |
| 209. C4 | #11924560 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924560 | 2 |
| #14558081 | 2 |
| #127×D37 | 2 |
| #14557921 | 2 |
| #14557909 | 2 |
| #14557906 | 2 |
| #14557905 | 2 |
| C4×#10596929 | 2 |
| C37×#493 | 2 |
| #3151 | 37 |