Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
826 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 826 conjugacy classes of subgroups — too many to draw. Only its 144 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. #14543879 | C2 | semidirect |
| 3. #14543878 | C2 | semidirect |
| 7. #11763790 | C4 | semidirect |
| 11. C2×#10587558 | C4 | semidirect |
| 12. C2×C4⋊C4×D17 | C4 | semidirect |
| 13. #11762716 | C4 | semidirect |
| 18. C17×#391 | C4 | semidirect |
| 48. #10587539 | C2×C4 | semidirect |
| 191. #391 | #595 | semidirect |
| 236. C17 | #12583 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763790 | 2 |
| #14543879 | 2 |
| #14543878 | 2 |
| #14531375 | 2 |
| #12583 | 17 |