Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
2122 conjugacy classes of subgroups.
The subgroup lattice has 360 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14537450 | C2 | semidirect |
| 2. #14537422 | C2 | semidirect |
| 3. #14537417 | C2 | semidirect |
| 4. C2×#11762833 | C2 | semidirect |
| 6. #14537203 | C2 | semidirect |
| 9. #11762870 | C22 | semidirect |
| 10. #11762866 | C22 | semidirect |
| 11. #11762862 | C22 | semidirect |
| 14. #11762833 | C22 | semidirect |
| 15. C2×C4⋊#3622 | C22 | semidirect |
| 18. #11762765 | C22 | semidirect |
| 254. C17 | #60125 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14537450 | 2 |
| #14537422 | 2 |
| #14537417 | 2 |
| C2×#11762833 | 2 |
| #14537229 | 2 |
| #14537203 | 2 |
| C2×C4×#41×C17 | 2 |
| #60125 | 17 |