Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 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. #14558350 | C2 | semidirect |
| 2. #14558338 | C2 | semidirect |
| 3. #14557976 | C2 | semidirect |
| 4. #14557971 | C2 | semidirect |
| 5. #14557965 | C2 | semidirect |
| 6. C2×#11924481 | C2 | semidirect |
| 7. C37×#504 | C2 | semidirect |
| 13. #11924558 | C22 | semidirect |
| 14. C2×Dic148 | C22 | semidirect |
| 16. Dic296 | C22 | semidirect |
| 17. #11924481 | C22 | semidirect |
| 18. #11924481 | C22 | semidirect |
| 19. #11924481 | C22 | semidirect |
| 20. D592 | C22 | semidirect |
| 22. M32×C37 | C22 | semidirect |
| 23. C2×C16×C37 | C22 | semidirect |
| 81. #504 | D37 | semidirect |
| 82. C37 | #3416 | semidirect |
| 97. M32 | C2×D37 | semidirect |
| 98. C2×C16 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558350 | 2 |
| #14558338 | 2 |
| #14557976 | 2 |
| #14557971 | 2 |
| #14557965 | 2 |
| C2×#11924481 | 2 |
| C37×#504 | 2 |
| #3416 | 37 |