Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
314 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 9. C22⋊#63216 | C4 | semidirect |
| 12. C22×#63214 | C4 | semidirect |
| 15. C22×C16×C17 | C4 | semidirect |
| 51. C22⋊#595 | C16 | semidirect |
| 128. C22×C16 | #595 | semidirect |
| 168. C17 | #7199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545009 | 2 |
| C8×C22⋊#595 | 2 |
| C2×#11762588 | 2 |
| #7199 | 17 |