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×#11924544 | C2 | semidirect |
| 3. #14558107 | C2 | semidirect |
| 4. #14557788 | C2 | semidirect |
| 5. #14557776 | C2 | semidirect |
| 6. #14557771 | C2 | semidirect |
| 7. #14557759 | C2 | semidirect |
| 8. #14557575 | C2 | semidirect |
| 9. #14557529 | C2 | semidirect |
| 10. C2×#11924460 | C2 | semidirect |
| 11. C2×#137×C37 | C2 | semidirect |
| 65. M16×C37 | D4 | semidirect |
| 144. C2×#137 | D37 | semidirect |
| 155. C37 | #3063 | semidirect |
| 210. M16 | C22⋊D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924544 | 2 |
| #14558111 | 2 |
| #14558107 | 2 |
| #14557788 | 2 |
| #14557776 | 2 |
| #14557771 | 2 |
| #14557759 | 2 |
| #14557575 | 2 |
| #14557529 | 2 |
| C2×#11924460 | 2 |
| C2×#137×C37 | 2 |
| #3063 | 37 |