Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
478 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 3. #14538824 | C2 | semidirect |
| 4. #14527421 | C2 | semidirect |
| 6. #14527127 | C2 | semidirect |
| 7. C17×#1287 | C2 | semidirect |
| 172. #1287 | D17 | semidirect |
| 270. C17 | #10041 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539797 | 2 |
| #14538907 | 2 |
| #14538824 | 2 |
| #14527421 | 2 |
| #14527254 | 2 |
| #14527127 | 2 |
| C17×#1287 | 2 |
| #10041 | 17 |