Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
788 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 788 conjugacy classes of subgroups — too many to draw. Only its 160 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 |
|---|---|---|
| 6. C4×C4⋊#595 | C4 | semidirect |
| 9. #11763745 | C4 | semidirect |
| 14. #11762832 | C4 | semidirect |
| 16. C4×#63223 | C4 | semidirect |
| 17. C4×M16×C17 | C4 | semidirect |
| 128. C4×M16 | #595 | semidirect |
| 164. C17 | #8048 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#10587677 | 2 |
| #14543664 | 2 |
| #14537415 | 2 |
| #8048 | 17 |