Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 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. #14558256 | C2 | semidirect |
| 3. #14557884 | C2 | semidirect |
| 4. #14557877 | C2 | semidirect |
| 5. #14557813 | C2 | semidirect |
| 6. #14557773 | C2 | semidirect |
| 7. #14557743 | C2 | semidirect |
| 8. #14557692 | C2 | semidirect |
| 9. C8×D148 | C2 | semidirect |
| 10. #14557526 | C2 | semidirect |
| 11. C4×SD16×C37 | C2 | semidirect |
| 134. C4×SD16 | D37 | semidirect |
| 137. C37 | #3302 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558256 | 2 |
| #14558187 | 2 |
| #14557884 | 2 |
| #14557877 | 2 |
| #14557813 | 2 |
| #14557773 | 2 |
| #14557743 | 2 |
| #14557692 | 2 |
| C8×D148 | 2 |
| #14557526 | 2 |
| C4×SD16×C37 | 2 |
| #3302 | 37 |