Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
386 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 113 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. #14558139 | C2 | semidirect |
| 2. #14558137 | C2 | semidirect |
| 3. #14557932 | C2 | semidirect |
| 4. #14557909 | C2 | semidirect |
| 5. #14557898 | C2 | semidirect |
| 6. #14557785 | C2 | semidirect |
| 7. #14557768 | C2 | semidirect |
| 8. #14557642 | C2 | semidirect |
| 9. #14557613 | C2 | semidirect |
| 10. #14557490 | C2 | semidirect |
| 11. C37×#490 | C2 | semidirect |
| 120. #490 | D37 | semidirect |
| 126. C37 | #3176 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558139 | 2 |
| #14558137 | 2 |
| #14557932 | 2 |
| #14557909 | 2 |
| #14557898 | 2 |
| #14557785 | 2 |
| #14557768 | 2 |
| #14557642 | 2 |
| #14557613 | 2 |
| #14557490 | 2 |
| C37×#490 | 2 |
| #3176 | 37 |