Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 2. #14557899 | C2 | semidirect |
| 3. #14557895 | C2 | semidirect |
| 4. #14557890 | C2 | semidirect |
| 5. #14557881 | C2 | semidirect |
| 6. #14557537 | C2 | semidirect |
| 7. #14557532 | C2 | semidirect |
| 8. #14557527 | C2 | semidirect |
| 9. C2×#11924456 | C2 | semidirect |
| 10. #14557489 | C2 | semidirect |
| 11. C37×#544 | C2 | semidirect |
| 21. #11924459 | C22 | semidirect |
| 22. #11924459 | C22 | semidirect |
| 23. #11924459 | C22 | semidirect |
| 28. #11924456 | C22 | semidirect |
| 29. #11924456 | C22 | semidirect |
| 30. #11924456 | C22 | semidirect |
| 31. #11924447 | C22 | semidirect |
| 32. C4×#64436 | C22 | semidirect |
| 34. C4⋊Q8×C37 | C22 | semidirect |
| 36. #125×C37 | C22 | semidirect |
| 136. #544 | D37 | semidirect |
| 147. C37 | #3136 | semidirect |
| 153. C4⋊Q8 | C2×D37 | semidirect |
| 156. #125 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558102 | 2 |
| #14557899 | 2 |
| #14557895 | 2 |
| #14557890 | 2 |
| #14557881 | 2 |
| #14557537 | 2 |
| #14557532 | 2 |
| #14557527 | 2 |
| C2×#11924456 | 2 |
| #14557489 | 2 |
| C37×#544 | 2 |
| #3136 | 37 |