Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
342 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 342 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 |
|---|---|---|
| 16. C4⋊#63214 | C4 | semidirect |
| 17. #11762627 | C4 | semidirect |
| 18. C17×C4⋊C16 | C4 | semidirect |
| 122. C4×C17 | #366 | semidirect |
| 126. Dic17 | #366 | semidirect |
| 140. C4⋊C16 | #595 | semidirect |
| 174. C17 | #13176 | semidirect |
| 251. C4 | #11763735 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763735 | 2 |
| #14544720 | 2 |
| C4×#10587534 | 2 |
| #14543842 | 2 |
| D17×C4⋊C16 | 2 |
| #13176 | 17 |