Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
306 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 16. C4⋊#63214 | C4 | semidirect |
| 17. #11762627 | C4 | semidirect |
| 18. C17×C4⋊C16 | C4 | semidirect |
| 113. C4×C17 | #365 | semidirect |
| 131. C4⋊C16 | #595 | semidirect |
| 163. C17 | #13185 | semidirect |
| 231. C4 | #11763734 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763734 | 2 |
| #14544723 | 2 |
| C4×#10587533 | 2 |
| #14543849 | 2 |
| #14530538 | 2 |
| #13185 | 17 |