Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
768 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 148 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 |
|---|---|---|
| 2. #14543873 | C2 | semidirect |
| 7. #11763788 | C4 | semidirect |
| 10. C2×#10587551 | C4 | semidirect |
| 12. C22×#63223 | C4 | semidirect |
| 13. #11762777 | C4 | semidirect |
| 17. C22×M16×C17 | C4 | semidirect |
| 40. C2×M16×C17 | C2×C4 | semidirect |
| 45. C22×#3622 | C2×C4 | semidirect |
| 47. #10587551 | C2×C4 | semidirect |
| 187. C22×M16 | #595 | semidirect |
| 224. C2×M16 | C2×#595 | semidirect |
| 240. C17 | #12577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763788 | 2 |
| #14543873 | 2 |
| #14537228 | 2 |
| #12577 | 17 |