Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
768 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 140 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. #14543873 | C2 | semidirect |
| 3. #14543872 | C2 | semidirect |
| 7. #11763789 | C4 | semidirect |
| 11. D17⋊#99 | C4 | semidirect |
| 13. C22×#63218 | C4 | semidirect |
| 14. C2×M16×D17 | C4 | semidirect |
| 16. #11762776 | C4 | semidirect |
| 20. C17×#408 | C4 | semidirect |
| 41. C2×M16×C17 | C2×C4 | semidirect |
| 42. C22×C8×C17 | C2×C4 | semidirect |
| 43. C2×#63223 | C2×C4 | semidirect |
| 44. C22×#3622 | C2×C4 | semidirect |
| 52. #10587551 | C2×C4 | semidirect |
| 213. #408 | #595 | semidirect |
| 241. C2×M16 | C2×#595 | semidirect |
| 244. C22×C8 | C2×#595 | semidirect |
| 260. C17 | #12577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D17⋊#410 | 2 |
| #14543873 | 2 |
| #14543872 | 2 |
| #14537226 | 2 |
| #12577 | 17 |