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. #14539160 | C2 | semidirect |
| 3. #14527497 | C2 | semidirect |
| 4. #14527382 | C2 | semidirect |
| 5. #14527296 | C2 | semidirect |
| 6. #14526676 | C2 | semidirect |
| 7. C17×#3215 | C2 | semidirect |
| 39. C17×C4⋊Q8 | D4 | semidirect |
| 40. C17×C4⋊Q8 | D4 | semidirect |
| 63. C17×C4⋊C8 | D4 | semidirect |
| 75. #10587474 | D4 | semidirect |
| 172. #3215 | D17 | semidirect |
| 240. C4⋊Q8 | C22⋊D17 | semidirect |
| 241. C4⋊Q8 | C22⋊D17 | semidirect |
| 264. C4⋊C8 | C22⋊D17 | semidirect |
| 277. C17 | #10096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539160 | 2 |
| #14534892 | 2 |
| #14527497 | 2 |
| #14527382 | 2 |
| #14527296 | 2 |
| #14526676 | 2 |
| C17×#3215 | 2 |
| #10096 | 17 |