Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
684 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 1. #14539789 | C2 | semidirect |
| 2. #14539159 | C2 | semidirect |
| 4. #14527497 | C2 | semidirect |
| 5. #14527381 | C2 | semidirect |
| 6. #14527295 | C2 | semidirect |
| 7. C17×#1300 | C2 | semidirect |
| 59. #10587555 | D4 | semidirect |
| 60. #10587555 | D4 | semidirect |
| 63. C17×C4⋊C8 | D4 | semidirect |
| 66. C17×#97 | D4 | semidirect |
| 178. #1300 | D17 | semidirect |
| 264. C4⋊C8 | D68 | semidirect |
| 273. #97 | D68 | semidirect |
| 277. C17 | #10096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539789 | 2 |
| #14539159 | 2 |
| #14534890 | 2 |
| #14527497 | 2 |
| #14527381 | 2 |
| #14527295 | 2 |
| C17×#1300 | 2 |
| #10096 | 17 |