Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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×#11924566 | C2 | semidirect |
| 2. C2×#11924543 | C2 | semidirect |
| 3. #14558104 | C2 | semidirect |
| 4. #14557789 | C2 | semidirect |
| 5. #14557777 | C2 | semidirect |
| 6. #14557772 | C2 | semidirect |
| 7. #14557760 | C2 | semidirect |
| 8. #14557573 | C2 | semidirect |
| 9. #14557529 | C2 | semidirect |
| 10. C2×#11924459 | C2 | semidirect |
| 79. #10596934 | D4 | semidirect |
| 155. C37 | #3063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924566 | 2 |
| C2×#11924543 | 2 |
| #14558104 | 2 |
| #14557789 | 2 |
| #14557777 | 2 |
| #14557772 | 2 |
| #14557760 | 2 |
| #14557573 | 2 |
| #14557529 | 2 |
| C2×#11924459 | 2 |
| C37×#537 | 2 |
| #3063 | 37 |