Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
616 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 116 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. #97×#595 | C2 | semidirect |
| 4. #14543661 | C2 | semidirect |
| 17. #11763665 | C4 | semidirect |
| 18. #11763664 | C4 | semidirect |
| 21. #11762549 | C4 | semidirect |
| 22. #11762548 | C4 | semidirect |
| 23. C17×#329 | C4 | semidirect |
| 51. #10587542 | C2×C4 | semidirect |
| 54. C17×#97 | C2×C4 | semidirect |
| 56. #10587474 | C2×C4 | semidirect |
| 164. #595 | #329 | direct (N × H) |
| 188. #329 | #595 | direct (N × H) |
| 225. #97 | C2×#595 | semidirect |
| 229. C17 | C4×#329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #124×#595 | 2 |
| #97×#595 | 2 |
| D17⋊#329 | 2 |
| #14543661 | 2 |
| D17×#329 | 2 |
| C4×#329 | 17 |