Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
724 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 134 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 |
|---|---|---|
| 1. C4×#10587543 | C2 | semidirect |
| 3. #14543960 | C2 | semidirect |
| 4. #14543657 | C2 | semidirect |
| 12. #11763660 | C4 | semidirect |
| 14. C2×D4×Dic17 | C4 | semidirect |
| 17. #11762707 | C4 | semidirect |
| 21. C4⋊C4×Dic17 | C4 | semidirect |
| 23. C17×#390 | C4 | semidirect |
| 55. (C2×#595)⋊C4 | C2×C4 | semidirect |
| 57. #10587543 | C2×C4 | semidirect |
| 230. #390 | #595 | semidirect |
| 290. C17 | #8220 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#10587543 | 2 |
| C2×#11763660 | 2 |
| #14543960 | 2 |
| #14543657 | 2 |
| #14531300 | 2 |
| #8220 | 17 |