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. #14558078 | C2 | semidirect |
| 2. #14557937 | C2 | semidirect |
| 3. #14557908 | C2 | semidirect |
| 4. #14557878 | C2 | semidirect |
| 5. #14557769 | C2 | semidirect |
| 6. #14557767 | C2 | semidirect |
| 7. D8×Dic37 | C2 | semidirect |
| 8. #14557615 | C2 | semidirect |
| 9. #14557613 | C2 | semidirect |
| 10. C2×C8×Dic37 | C2 | semidirect |
| 11. C37×#466 | C2 | semidirect |
| 89. C2×Dic37 | D8 | semidirect |
| 99. C8×C37 | #41 | semidirect |
| 101. #64436 | #41 | semidirect |
| 134. #466 | D37 | semidirect |
| 139. C37 | #3169 | semidirect |
| 229. C8 | #10596964 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558078 | 2 |
| #14557937 | 2 |
| #14557908 | 2 |
| #14557878 | 2 |
| #14557769 | 2 |
| #14557767 | 2 |
| D8×Dic37 | 2 |
| #14557615 | 2 |
| #14557613 | 2 |
| C2×C8×Dic37 | 2 |
| C37×#466 | 2 |
| #3169 | 37 |