Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
490 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #14527297 | C2 | semidirect |
| 5. #14527295 | C2 | semidirect |
| 6. #14526678 | C2 | semidirect |
| 7. C17×#1300 | C2 | semidirect |
| 10. #11763169 | C4 | semidirect |
| 11. #11763169 | C4 | semidirect |
| 53. #10587555 | C2×C4 | semidirect |
| 54. #10587555 | C2×C4 | semidirect |
| 60. C17×#97 | C2×C4 | semidirect |
| 179. #1300 | D17 | semidirect |
| 270. #97 | C4×D17 | semidirect |
| 280. C17 | #9439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539171 | 2 |
| #14531894 | 2 |
| #14527407 | 2 |
| #14527297 | 2 |
| #14527295 | 2 |
| #14526678 | 2 |
| C17×#1300 | 2 |
| #9439 | 17 |