Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
318 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 10. #11763738 | C4 | semidirect |
| 11. C16×#595 | C4 | semidirect |
| 15. #11762637 | C4 | semidirect |
| 16. #11762634 | C4 | semidirect |
| 17. C17×#367 | C4 | semidirect |
| 106. #367 | #595 | semidirect |
| 135. C17 | #12670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763738 | 2 |
| C2×C16×#595 | 2 |
| #14544588 | 2 |
| #14543845 | 2 |
| #14530567 | 2 |
| #12670 | 17 |