Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×C4×Dic74 | C2 | semidirect |
| 2. #14557866 | C2 | semidirect |
| 4. #14557837 | C2 | semidirect |
| 5. #14557752 | C2 | semidirect |
| 6. #14557688 | C2 | semidirect |
| 8. #14557638 | C2 | semidirect |
| 9. #14557633 | C2 | semidirect |
| 10. #14557590 | C2 | semidirect |
| 143. C37 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic74 | 2 |
| #14557866 | 2 |
| #14557849 | 2 |
| #14557837 | 2 |
| #14557752 | 2 |
| #14557688 | 2 |
| #14557671 | 2 |
| #14557638 | 2 |
| #14557633 | 2 |
| #14557590 | 2 |
| C37×#529 | 2 |
| #3117 | 37 |