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 |
| 3. #14557898 | C2 | semidirect |
| 4. #14557893 | C2 | semidirect |
| 5. #14557888 | C2 | semidirect |
| 6. #14557880 | C2 | semidirect |
| 7. #14557539 | C2 | semidirect |
| 8. #14557535 | C2 | semidirect |
| 9. #14557530 | C2 | semidirect |
| 10. C2×#11924458 | C2 | semidirect |
| 11. C37×#405 | C2 | semidirect |
| 14. #11924536 | C22 | semidirect |
| 17. #11924528 | C22 | semidirect |
| 26. #11924461 | C22 | semidirect |
| 27. #11924461 | C22 | semidirect |
| 28. #11924461 | C22 | semidirect |
| 33. #11924458 | C22 | semidirect |
| 34. #11924458 | C22 | semidirect |
| 35. #11924458 | C22 | semidirect |
| 39. #97×C37 | C22 | semidirect |
| 40. C4×C8×C37 | C22 | semidirect |
| 146. #405 | D37 | semidirect |
| 147. C37 | #3136 | semidirect |
| 175. #97 | C2×D37 | semidirect |
| 176. C4×C8 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558161 | 2 |
| #14558102 | 2 |
| #14557898 | 2 |
| #14557893 | 2 |
| #14557888 | 2 |
| #14557880 | 2 |
| #14557539 | 2 |
| #14557535 | 2 |
| #14557530 | 2 |
| C2×#11924458 | 2 |
| C37×#405 | 2 |
| #3136 | 37 |