Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
460 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 3. #14544543 | C2 | semidirect |
| 4. #14543886 | C2 | semidirect |
| 6. C2×#10587680 | C4 | semidirect |
| 10. #11763813 | C4 | semidirect |
| 12. #11763784 | C4 | semidirect |
| 15. C4×#63242 | C4 | semidirect |
| 21. #11762608 | C4 | semidirect |
| 22. #11762605 | C4 | semidirect |
| 23. C17×#356 | C4 | semidirect |
| 169. #356 | #595 | semidirect |
| 214. C17 | #12633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545509 | 2 |
| #14545058 | 2 |
| #14544543 | 2 |
| #14543886 | 2 |
| #14530468 | 2 |
| #12633 | 17 |