Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
554 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 139 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. #14529613 | C2 | semidirect |
| 2. C4×C8×Dic17 | C2 | semidirect |
| 3. #14527543 | C2 | semidirect |
| 4. #14527235 | C2 | semidirect |
| 14. C17×#500 | C4 | semidirect |
| 15. C17×#493 | C4 | semidirect |
| 16. C17×#486 | C4 | semidirect |
| 74. C4×Dic17 | D8 | semidirect |
| 104. C8×C17 | #104 | semidirect |
| 129. #500 | Dic17 | semidirect |
| 130. #493 | Dic17 | semidirect |
| 131. #486 | Dic17 | semidirect |
| 174. C17 | #9844 | semidirect |
| 233. C8 | #10587508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14529613 | 2 |
| C4×C8×Dic17 | 2 |
| #14527543 | 2 |
| #14527235 | 2 |
| C17×#3169 | 2 |
| #9844 | 17 |