Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
460 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 127 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×Q16×D37 | C2 | semidirect |
| 4. #14557792 | C2 | semidirect |
| 5. #14557791 | C2 | semidirect |
| 6. #14557788 | C2 | semidirect |
| 7. #14557773 | C2 | semidirect |
| 8. #14557772 | C2 | semidirect |
| 9. #14557568 | C2 | semidirect |
| 10. #14557540 | C2 | semidirect |
| 11. C37×#470 | C2 | semidirect |
| 140. #470 | D37 | semidirect |
| 145. C37 | #3059 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D37 | 2 |
| C2×#11924544 | 2 |
| #14558106 | 2 |
| #14557792 | 2 |
| #14557791 | 2 |
| #14557788 | 2 |
| #14557773 | 2 |
| #14557772 | 2 |
| #14557568 | 2 |
| #14557540 | 2 |
| C37×#470 | 2 |
| #3059 | 37 |