Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
452 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 123 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. #14558332 | C2 | semidirect |
| 2. C2×#11924559 | C2 | semidirect |
| 3. #131×D37 | C2 | semidirect |
| 4. #14557805 | C2 | semidirect |
| 5. #14557804 | C2 | semidirect |
| 6. #14557803 | C2 | semidirect |
| 7. #14557799 | C2 | semidirect |
| 8. #14557798 | C2 | semidirect |
| 9. #108×D37 | C2 | semidirect |
| 10. #14557516 | C2 | semidirect |
| 11. C37×#473 | C2 | semidirect |
| 25. C2×#10596941 | C22 | semidirect |
| 26. C2×D296 | C22 | semidirect |
| 37. #11924472 | C22 | semidirect |
| 38. #11924471 | C22 | semidirect |
| 39. #11924455 | C22 | semidirect |
| 40. #11924452 | C22 | semidirect |
| 41. #11924452 | C22 | semidirect |
| 43. C2×Q16×C37 | C22 | semidirect |
| 45. #108×C37 | C22 | semidirect |
| 46. #101×C37 | C22 | semidirect |
| 171. #473 | D37 | semidirect |
| 178. C37 | #3067 | semidirect |
| 193. C2×Q16 | C2×D37 | semidirect |
| 209. #108 | C2×D37 | semidirect |
| 211. #101 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558332 | 2 |
| C2×#11924559 | 2 |
| #131×D37 | 2 |
| #14557805 | 2 |
| #14557804 | 2 |
| #14557803 | 2 |
| #14557799 | 2 |
| #14557798 | 2 |
| #108×D37 | 2 |
| #14557516 | 2 |
| C37×#473 | 2 |
| #3067 | 37 |