Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
336 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 56 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 |
|---|---|---|
| 3. #14543923 | C2 | semidirect |
| 4. #14543917 | C2 | semidirect |
| 13. #11763201 | C4 | semidirect |
| 16. #11763166 | C4 | semidirect |
| 21. #11762870 | C4 | semidirect |
| 22. C17×#541 | C4 | semidirect |
| 27. C17×C4⋊Q8 | C2×C4 | semidirect |
| 30. C17×#125 | C2×C4 | semidirect |
| 54. #10587474 | C2×C4 | semidirect |
| 55. C4×#3622 | C2×C4 | semidirect |
| 153. #541 | #595 | semidirect |
| 182. C4⋊Q8 | C2×#595 | semidirect |
| 187. #125 | C2×#595 | semidirect |
| 209. C17 | #13610 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545065 | 2 |
| #14545061 | 2 |
| #14543923 | 2 |
| #14543917 | 2 |
| #14539850 | 2 |
| #13610 | 17 |