Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
528 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 528 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. C4⋊Q8×D37 | C2 | semidirect |
| 3. #14557881 | C2 | semidirect |
| 4. #14557880 | C2 | semidirect |
| 5. #14557879 | C2 | semidirect |
| 6. #14557878 | C2 | semidirect |
| 7. #102×D37 | C2 | semidirect |
| 8. C4×C8×D37 | C2 | semidirect |
| 9. C37×#486 | C2 | semidirect |
| 15. #11924536 | C22 | semidirect |
| 17. #11924535 | C22 | semidirect |
| 26. #11924458 | C22 | semidirect |
| 27. #11924457 | C22 | semidirect |
| 28. #11924456 | C22 | semidirect |
| 29. C4×#64436 | C22 | semidirect |
| 30. C8×Dic37 | C22 | semidirect |
| 31. C4⋊Q8×C37 | C22 | semidirect |
| 33. #102×C37 | C22 | semidirect |
| 34. C4×C8×C37 | C22 | semidirect |
| 126. D37 | #486 | direct (N × H) |
| 133. #486 | D37 | direct (N × H) |
| 136. C37 | C2×#486 | semidirect |
| 146. C4⋊Q8 | C2×D37 | semidirect |
| 158. #102 | C2×D37 | semidirect |
| 161. C4×C8 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D37 | 2 |
| #127×D37 | 2 |
| #14557881 | 2 |
| #14557880 | 2 |
| #14557879 | 2 |
| #14557878 | 2 |
| #102×D37 | 2 |
| C4×C8×D37 | 2 |
| C37×#486 | 2 |
| C2×#486 | 37 |