Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
372 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 133 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. #14558161 | C2 | semidirect |
| 3. #14557902 | C2 | semidirect |
| 4. #14557893 | C2 | semidirect |
| 5. #14557888 | C2 | semidirect |
| 6. #14557884 | C2 | semidirect |
| 7. #14557543 | C2 | semidirect |
| 10. C2×#11924461 | C2 | semidirect |
| 11. C37×#405 | C2 | semidirect |
| 138. #405 | D37 | semidirect |
| 139. C37 | #3137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558161 | 2 |
| #14558109 | 2 |
| #14557902 | 2 |
| #14557893 | 2 |
| #14557888 | 2 |
| #14557884 | 2 |
| #14557543 | 2 |
| #14557535 | 2 |
| #14557530 | 2 |
| C2×#11924461 | 2 |
| C37×#405 | 2 |
| #3137 | 37 |