Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#10596941 | C2 | semidirect |
| 2. C2×#11924543 | C2 | semidirect |
| 4. #14557781 | C2 | semidirect |
| 5. #14557764 | C2 | semidirect |
| 6. #14557569 | C2 | semidirect |
| 7. #14557542 | C2 | semidirect |
| 8. #14557537 | C2 | semidirect |
| 9. C37×#536 | C2 | semidirect |
| 16. C2×#10596934 | C22 | semidirect |
| 18. C22×#64436 | C22 | semidirect |
| 24. #11924469 | C22 | semidirect |
| 25. #11924467 | C22 | semidirect |
| 26. #11924460 | C22 | semidirect |
| 33. C22⋊Q8×C37 | C22 | semidirect |
| 67. C2×#64436 | D4 | semidirect |
| 123. #536 | D37 | semidirect |
| 130. C37 | #3057 | semidirect |
| 147. C22⋊Q8 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596941 | 2 |
| C2×#11924543 | 2 |
| #14558097 | 2 |
| #14557781 | 2 |
| #14557764 | 2 |
| #14557569 | 2 |
| #14557542 | 2 |
| #14557537 | 2 |
| C37×#536 | 2 |
| #3057 | 37 |