Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
500 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 197 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 |
|---|---|---|
| 2. C4×#10596962 | C2 | semidirect |
| 3. C4×Dic148 | C2 | semidirect |
| 4. C4×#10596930 | C2 | semidirect |
| 5. C4×D296 | C2 | semidirect |
| 6. #14557571 | C2 | semidirect |
| 7. #14557530 | C2 | semidirect |
| 8. C2×C4×C8×C37 | C2 | semidirect |
| 10. #11924558 | C4 | direct (N × H) |
| 33. #10596962 | C2×C4 | semidirect |
| 39. C2×C8×C37 | C2×C4 | semidirect |
| 52. Dic148 | C2×C4 | semidirect |
| 53. D296 | C2×C4 | semidirect |
| 54. #10596930 | C2×C4 | semidirect |
| 83. C4×C37 | #135 | semidirect |
| 100. C2×C4×C8 | D37 | semidirect |
| 101. C37 | C4×#135 | semidirect |
| 135. C2×C8 | C4×D37 | semidirect |
| 178. C4 | #11924558 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924558 | 2 |
| C4×#10596962 | 2 |
| C4×Dic148 | 2 |
| C4×#10596930 | 2 |
| C4×D296 | 2 |
| #14557571 | 2 |
| #14557530 | 2 |
| C2×C4×C8×C37 | 2 |
| C4×#135 | 37 |