Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
350 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 160 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 |
|---|---|---|
| 8. #11763702 | C4 | semidirect |
| 9. #11763701 | C4 | semidirect |
| 10. #11763700 | C4 | semidirect |
| 11. #11763699 | C4 | semidirect |
| 12. #11763696 | C4 | semidirect |
| 13. C16×#595 | C4 | semidirect |
| 20. #11762585 | C4 | semidirect |
| 21. #11762584 | C4 | semidirect |
| 22. C16×Dic17 | C4 | semidirect |
| 23. C4×C16×C17 | C4 | semidirect |
| 114. C4×C16 | #595 | semidirect |
| 143. C17 | #12542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545006 | 2 |
| #14545003 | 2 |
| #14544992 | 2 |
| #14544505 | 2 |
| #14530379 | 2 |
| #12542 | 17 |