Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
460 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 121 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. #14528587 | C2 | semidirect |
| 4. #14526914 | C2 | semidirect |
| 6. C2×#10587634 | C4 | semidirect |
| 10. #11762833 | C4 | semidirect |
| 12. #11762776 | C4 | semidirect |
| 15. C2×C4×#3622 | C4 | semidirect |
| 21. C17×#356 | C4 | semidirect |
| 22. C17×#355 | C4 | semidirect |
| 164. #356 | Dic17 | semidirect |
| 165. #355 | Dic17 | semidirect |
| 208. C17 | #12633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14537496 | 2 |
| #14530449 | 2 |
| #14528587 | 2 |
| #14526914 | 2 |
| C17×#2132 | 2 |
| #12633 | 17 |