Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
174 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 59 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. #14557615 | C2 | semidirect |
| 3. #14557333 | C2 | semidirect |
| 4. C16×Dic37 | C2 | semidirect |
| 5. C37×#366 | C2 | semidirect |
| 8. D592 | C4 | semidirect |
| 22. D296 | C2×C4 | semidirect |
| 23. C16×C37 | C2×C4 | semidirect |
| 44. Dic37 | D16 | semidirect |
| 52. #366 | D37 | semidirect |
| 55. C37 | C4×D16 | semidirect |
| 74. C16 | C4×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D592 | 2 |
| #14557615 | 2 |
| #14557333 | 2 |
| C16×Dic37 | 2 |
| C37×#366 | 2 |
| C4×D16 | 37 |