Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 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. #14558186 | C2 | semidirect |
| 2. D4×D148 | C2 | semidirect |
| 3. #14557881 | C2 | semidirect |
| 4. #14557848 | C2 | semidirect |
| 5. #14557770 | C2 | semidirect |
| 6. #14557729 | C2 | semidirect |
| 7. #14557668 | C2 | semidirect |
| 8. C4×#10596939 | C2 | semidirect |
| 9. #14557598 | C2 | semidirect |
| 10. #102×D37 | C2 | semidirect |
| 11. C37×#474 | C2 | semidirect |
| 15. C2×D296 | C22 | semidirect |
| 17. C2×C8×D37 | C22 | semidirect |
| 22. #11924511 | C22 | semidirect |
| 26. C4×D148 | C22 | semidirect |
| 27. C4⋊C4×D37 | C22 | semidirect |
| 28. #11924469 | C22 | semidirect |
| 29. #11924458 | C22 | semidirect |
| 31. #11924456 | C22 | semidirect |
| 32. #11924456 | C22 | semidirect |
| 33. #11924456 | C22 | semidirect |
| 34. #11924448 | C22 | semidirect |
| 35. C4×#64436 | C22 | semidirect |
| 36. C4⋊Q8×C37 | C22 | semidirect |
| 38. #107×C37 | C22 | semidirect |
| 39. C4⋊C8×C37 | C22 | semidirect |
| 87. D4×C37 | #41 | semidirect |
| 105. D148 | D8 | semidirect |
| 147. #474 | D37 | semidirect |
| 154. C37 | #3294 | semidirect |
| 161. C4⋊Q8 | C2×D37 | semidirect |
| 174. #107 | C2×D37 | semidirect |
| 175. C4⋊C8 | C2×D37 | semidirect |
| 240. D4 | #10596966 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558186 | 2 |
| D4×D148 | 2 |
| #14557881 | 2 |
| #14557848 | 2 |
| #14557770 | 2 |
| #14557729 | 2 |
| #14557668 | 2 |
| C4×#10596939 | 2 |
| #14557598 | 2 |
| #102×D37 | 2 |
| C37×#474 | 2 |
| #3294 | 37 |