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. #14543918 | C2 | semidirect |
| 3. #14543916 | C2 | semidirect |
| 9. #11763359 | C4 | semidirect |
| 12. #11763186 | C4 | semidirect |
| 14. #11763182 | C4 | semidirect |
| 16. C4×M16×C17 | C4 | semidirect |
| 33. #10587560 | C2×C4 | semidirect |
| 37. #10587555 | C2×C4 | semidirect |
| 41. C4×C8×C17 | C2×C4 | semidirect |
| 42. C4×C8×C17 | C2×C4 | semidirect |
| 138. C4×M16 | #595 | semidirect |
| 171. C4×C8 | C2×#595 | semidirect |
| 172. C4×C8 | 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 |
| #14543918 | 2 |
| #14543916 | 2 |
| #14539236 | 2 |
| #13584 | 17 |