Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
826 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 826 conjugacy classes of subgroups — too many to draw. Only its 152 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 |
| 6. #11763788 | C4 | semidirect |
| 10. C2×#10587612 | C4 | semidirect |
| 11. #11762714 | C4 | semidirect |
| 15. C22×C4⋊C4×C17 | C4 | semidirect |
| 42. #10587539 | C2×C4 | semidirect |
| 165. C22×C4⋊C4 | #595 | semidirect |
| 210. C17 | #12583 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763788 | 2 |
| #14543879 | 2 |
| #14531377 | 2 |
| #12583 | 17 |