Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
592 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 12. C2×#10587574 | C4 | semidirect |
| 16. #11762707 | C4 | semidirect |
| 18. #11762678 | C4 | semidirect |
| 22. C17×#389 | C4 | semidirect |
| 50. (C2×#595)⋊C4 | Q8 | semidirect |
| 204. #389 | #595 | semidirect |
| 256. C17 | #9911 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544639 | 2 |
| #14543960 | 2 |
| #14543657 | 2 |
| #14537135 | 2 |
| #9911 | 17 |