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 |
|---|---|---|
| 1. #14558161 | C2 | semidirect |
| 2. #14557897 | C2 | semidirect |
| 3. #14557892 | C2 | semidirect |
| 4. #14557887 | C2 | semidirect |
| 5. #14557879 | C2 | semidirect |
| 6. #14557538 | C2 | semidirect |
| 7. #14557534 | C2 | semidirect |
| 8. #14557529 | C2 | semidirect |
| 9. C2×#11924457 | C2 | semidirect |
| 10. #14557489 | C2 | semidirect |
| 14. #11924536 | C22 | semidirect |
| 16. #11924528 | C22 | semidirect |
| 21. #11924460 | C22 | semidirect |
| 22. #11924460 | C22 | semidirect |
| 23. #11924460 | C22 | semidirect |
| 28. #11924457 | C22 | semidirect |
| 29. #11924457 | C22 | semidirect |
| 30. #11924457 | C22 | semidirect |
| 31. #11924447 | C22 | semidirect |
| 32. C4×#64436 | C22 | semidirect |
| 147. C37 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558161 | 2 |
| #14557897 | 2 |
| #14557892 | 2 |
| #14557887 | 2 |
| #14557879 | 2 |
| #14557538 | 2 |
| #14557534 | 2 |
| #14557529 | 2 |
| C2×#11924457 | 2 |
| #14557489 | 2 |
| C37×#535 | 2 |
| #3136 | 37 |