Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
388 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 388 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 |
|---|---|---|
| 4. C22×#63243 | C4 | semidirect |
| 7. C2×#10587543 | C4 | semidirect |
| 14. #11762578 | C4 | semidirect |
| 15. C17×#343 | C4 | semidirect |
| 161. #343 | #595 | semidirect |
| 196. C17 | #7282 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544764 | 2 |
| #14544529 | 2 |
| #14528575 | 2 |
| #7282 | 17 |