Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
782 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 782 conjugacy classes of subgroups — too many to draw. Only its 142 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. C2×M16×D17 | C4 | semidirect |
| 14. C22×C8×D17 | C4 | semidirect |
| 16. #11762776 | C4 | semidirect |
| 20. C17×#408 | C4 | semidirect |
| 43. C2×M16×C17 | C2×C4 | semidirect |
| 44. C22×C8×C17 | C2×C4 | semidirect |
| 45. C2×#63223 | C2×C4 | semidirect |
| 46. C22×#3622 | C2×C4 | semidirect |
| 56. #10587551 | C2×C4 | semidirect |
| 234. #408 | #595 | semidirect |
| 243. D17 | #1391 | semidirect |
| 263. C2×M16 | C2×#595 | semidirect |
| 270. C22×C8 | C2×#595 | semidirect |
| 286. C17 | C2×#1391 | 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 |
| D17×#408 | 2 |
| C2×#1391 | 17 |