Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 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. #14558080 | C2 | semidirect |
| 2. #14557937 | C2 | semidirect |
| 3. #14557908 | C2 | semidirect |
| 4. #14557878 | C2 | semidirect |
| 5. #14557770 | C2 | semidirect |
| 6. #14557768 | C2 | semidirect |
| 7. #14557766 | C2 | semidirect |
| 8. C4×D296 | C2 | semidirect |
| 9. C4×#10596939 | C2 | semidirect |
| 10. C4×C8×D37 | C2 | semidirect |
| 11. C4×D8×C37 | C2 | semidirect |
| 96. C4×D37 | D8 | semidirect |
| 99. C8×C37 | #41 | semidirect |
| 101. #64436 | #41 | semidirect |
| 137. C4×D8 | D37 | semidirect |
| 139. C37 | #3169 | semidirect |
| 229. C8 | #10596962 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558080 | 2 |
| #14557937 | 2 |
| #14557908 | 2 |
| #14557878 | 2 |
| #14557770 | 2 |
| #14557768 | 2 |
| #14557766 | 2 |
| C4×D296 | 2 |
| C4×#10596939 | 2 |
| C4×C8×D37 | 2 |
| C4×D8×C37 | 2 |
| #3169 | 37 |