Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
318 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 9. #11763738 | C4 | semidirect |
| 10. #11763737 | C4 | semidirect |
| 11. #11763736 | C4 | semidirect |
| 12. #11763735 | C4 | semidirect |
| 17. C4×#63214 | C4 | semidirect |
| 18. C16×Dic17 | C4 | semidirect |
| 19. C16×Dic17 | C4 | semidirect |
| 20. C4×C16×C17 | C4 | semidirect |
| 125. C4×C16 | #595 | semidirect |
| 156. C17 | #12670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D17⋊#368 | 2 |
| #14545135 | 2 |
| #14544586 | 2 |
| #14543846 | 2 |
| C4×C16×D17 | 2 |
| #12670 | 17 |