Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
306 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 21. C4⋊#63214 | C4 | semidirect |
| 22. #11762627 | C4 | semidirect |
| 23. #11762627 | C4 | semidirect |
| 24. C17×C4⋊C16 | C4 | semidirect |
| 138. Dic17 | #365 | semidirect |
| 156. C4⋊C16 | #595 | semidirect |
| 195. C17 | #13185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763734 | 2 |
| C2×#11763733 | 2 |
| #14544724 | 2 |
| C4×#10587533 | 2 |
| #14543849 | 2 |
| #14530538 | 2 |
| #13185 | 17 |