Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #14558240 | C2 | semidirect |
| 2. #14558203 | C2 | semidirect |
| 3. #14557896 | C2 | semidirect |
| 4. #14557879 | C2 | semidirect |
| 5. #14557835 | C2 | semidirect |
| 6. #14557824 | C2 | semidirect |
| 7. #14557726 | C2 | semidirect |
| 8. #14557660 | C2 | semidirect |
| 9. #14557645 | C2 | semidirect |
| 10. C4×#10596939 | C2 | semidirect |
| 11. C37×#459 | C2 | semidirect |
| 82. D4×C37 | #41 | semidirect |
| 137. #459 | D37 | semidirect |
| 141. C37 | #3366 | semidirect |
| 218. D4 | #10596964 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558240 | 2 |
| #14558203 | 2 |
| #14557896 | 2 |
| #14557879 | 2 |
| #14557835 | 2 |
| #14557824 | 2 |
| #14557726 | 2 |
| #14557660 | 2 |
| #14557645 | 2 |
| C4×#10596939 | 2 |
| C37×#459 | 2 |
| #3366 | 37 |