Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
370 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 370 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. #14558338 | C2 | semidirect |
| 2. #14557971 | C2 | semidirect |
| 3. #14557965 | C2 | semidirect |
| 4. C2×D592 | C2 | semidirect |
| 5. C37×#504 | C2 | semidirect |
| 8. #11924558 | C22 | semidirect |
| 9. C2×D296 | C22 | semidirect |
| 10. Dic296 | C22 | semidirect |
| 11. #11924481 | C22 | semidirect |
| 12. D592 | C22 | semidirect |
| 13. D592 | C22 | semidirect |
| 15. M32×C37 | C22 | semidirect |
| 16. C2×C16×C37 | C22 | semidirect |
| 55. #504 | D37 | semidirect |
| 56. C37 | #3415 | semidirect |
| 66. M32 | C2×D37 | semidirect |
| 67. C2×C16 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558338 | 2 |
| #14557971 | 2 |
| #14557965 | 2 |
| C2×D592 | 2 |
| C37×#504 | 2 |
| #3415 | 37 |