Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
564 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×#10596941 | C2 | semidirect |
| 2. C22×C8×D37 | C2 | semidirect |
| 3. C2×#11924512 | C2 | semidirect |
| 5. #14557765 | C2 | direct (N × H) |
| 6. C2×#11924467 | C2 | semidirect |
| 7. C2×#11924458 | C2 | semidirect |
| 8. C2×#103×C37 | C2 | semidirect |
| 13. C2×#10596941 | C22 | semidirect |
| 16. C2×C8×D37 | C22 | semidirect |
| 18. #11924512 | C22 | semidirect |
| 25. #11924467 | C22 | semidirect |
| 26. #11924458 | C22 | semidirect |
| 30. #103×C37 | C22 | semidirect |
| 62. C2×#64436 | D4 | semidirect |
| 72. C22×D37 | SD16 | semidirect |
| 97. #64436 | C2×D4 | semidirect |
| 109. C2×D37 | C2×SD16 | semidirect |
| 118. C2×C37 | #465 | semidirect |
| 130. C2×#103 | D37 | semidirect |
| 132. C37 | C2×#465 | semidirect |
| 153. #103 | C2×D37 | semidirect |
| 243. C2 | #14557765 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596941 | 2 |
| C22×C8×D37 | 2 |
| C2×#11924512 | 2 |
| C2×#11924511 | 2 |
| #14557765 | 2 |
| C2×#11924467 | 2 |
| C2×#11924458 | 2 |
| C2×#103×C37 | 2 |
| C2×#465 | 37 |