Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
712 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 126 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. #14544511 | C2 | semidirect |
| 3. #14543960 | C2 | semidirect |
| 4. #14543657 | C2 | semidirect |
| 12. #11763660 | C4 | semidirect |
| 16. #11762712 | C4 | semidirect |
| 17. #11762705 | C4 | semidirect |
| 21. C4×C4⋊Dic17 | C4 | semidirect |
| 23. C2×C4×D4×C17 | C4 | semidirect |
| 54. (C2×#595)⋊C4 | C2×C4 | semidirect |
| 56. #10587543 | C2×C4 | semidirect |
| 224. C2×C4×D4 | #595 | semidirect |
| 287. C17 | #8216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544511 | 2 |
| C2×#11763660 | 2 |
| #14543960 | 2 |
| #14543657 | 2 |
| C4×#10587624 | 2 |
| #8216 | 17 |