Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
474 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 60 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 |
|---|---|---|
| 1. C2×#11763714 | C2 | semidirect |
| 2. #14543917 | C2 | semidirect |
| 3. #14543915 | C2 | semidirect |
| 11. #11763185 | C4 | semidirect |
| 13. #11763183 | C4 | semidirect |
| 15. C4×#63223 | C4 | semidirect |
| 16. C17×#532 | C4 | semidirect |
| 21. C17×C4⋊Q8 | C2×C4 | semidirect |
| 22. C17×#127 | C2×C4 | semidirect |
| 41. C4×#3622 | C2×C4 | semidirect |
| 42. C4×#3622 | C2×C4 | semidirect |
| 130. #532 | #595 | semidirect |
| 157. C4⋊Q8 | C2×#595 | semidirect |
| 162. #127 | C2×#595 | semidirect |
| 173. C17 | #13584 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763714 | 2 |
| #14543917 | 2 |
| #14543915 | 2 |
| #14539237 | 2 |
| #13584 | 17 |