Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
500 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 127 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×#11924559 | C2 | semidirect |
| 2. C2×M16×D37 | C2 | semidirect |
| 3. #14558046 | C2 | semidirect |
| 4. #14557788 | C2 | semidirect |
| 5. #14557787 | C2 | semidirect |
| 6. #14557786 | C2 | semidirect |
| 7. #14557782 | C2 | semidirect |
| 8. #14557781 | C2 | semidirect |
| 9. #14557568 | C2 | semidirect |
| 10. #14557528 | C2 | semidirect |
| 11. C37×#470 | C2 | semidirect |
| 15. C2×#10596941 | C22 | semidirect |
| 16. C2×D296 | C22 | semidirect |
| 31. #11924469 | C22 | semidirect |
| 32. #11924468 | C22 | semidirect |
| 33. #11924460 | C22 | semidirect |
| 34. #11924458 | C22 | semidirect |
| 35. #11924456 | C22 | semidirect |
| 36. C2×Q16×C37 | C22 | semidirect |
| 39. #106×C37 | C22 | semidirect |
| 40. #103×C37 | C22 | semidirect |
| 80. C8×D37 | D4 | semidirect |
| 145. #470 | D37 | semidirect |
| 152. C37 | #3054 | semidirect |
| 156. C2×Q16 | C2×D37 | semidirect |
| 177. #106 | C2×D37 | semidirect |
| 179. #103 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924559 | 2 |
| C2×M16×D37 | 2 |
| #14558046 | 2 |
| #14557788 | 2 |
| #14557787 | 2 |
| #14557786 | 2 |
| #14557782 | 2 |
| #14557781 | 2 |
| #14557568 | 2 |
| #14557528 | 2 |
| C37×#470 | 2 |
| #3054 | 37 |