Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
878 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 878 conjugacy classes of subgroups — too many to draw. Only its 95 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. #14537823 | C2 | semidirect |
| 3. #14528705 | C2 | semidirect |
| 4. #14527120 | C2 | semidirect |
| 5. #14526691 | C2 | semidirect |
| 6. #14526689 | C2 | semidirect |
| 7. C17×#1783 | C2 | semidirect |
| 42. C2×M16×C17 | D4 | semidirect |
| 59. C2×#63223 | D4 | semidirect |
| 196. C2×Dic17 | #100 | semidirect |
| 206. #1783 | D17 | semidirect |
| 293. C2×M16 | C22⋊D17 | semidirect |
| 323. C17 | #9504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14537823 | 2 |
| #14532134 | 2 |
| #14528705 | 2 |
| #14527120 | 2 |
| #14526691 | 2 |
| #14526689 | 2 |
| C17×#1783 | 2 |
| #9504 | 17 |