Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1114 conjugacy classes of subgroups; only the 380 normal subgroups are shown.
This group has 1114 conjugacy classes of subgroups — too many to draw. Only its 380 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. #14545751 | C2 | semidirect |
| 2. C2×#11763867 | C2 | semidirect |
| 3. #14545026 | C2 | semidirect |
| 4. C2×#11763707 | C2 | semidirect |
| 8. C2×#10587538 | C22 | semidirect |
| 9. C2×#10587538 | C22 | semidirect |
| 10. C22×#63216 | C22 | semidirect |
| 11. #11763707 | C22 | semidirect |
| 12. #11763707 | C22 | semidirect |
| 162. C17 | #33340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545751 | 2 |
| C2×#11763867 | 2 |
| #14545026 | 2 |
| C2×#11763707 | 2 |
| #14543496 | 2 |
| #33340 | 17 |