Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
798 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 159 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. #14539908 | C2 | semidirect |
| 2. #14539712 | C2 | semidirect |
| 3. #14539520 | C2 | semidirect |
| 4. #14539238 | C2 | semidirect |
| 5. #14528445 | C2 | semidirect |
| 6. #14528417 | C2 | semidirect |
| 7. #14528410 | C2 | semidirect |
| 8. #14528389 | C2 | semidirect |
| 9. #14528370 | C2 | semidirect |
| 10. #14527082 | C2 | semidirect |
| 11. C17×#1721 | C2 | semidirect |
| 169. #1721 | D17 | semidirect |
| 273. C17 | #19721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539908 | 2 |
| #14539712 | 2 |
| #14539520 | 2 |
| #14539238 | 2 |
| #14528445 | 2 |
| #14528417 | 2 |
| #14528410 | 2 |
| #14528389 | 2 |
| #14528370 | 2 |
| #14527082 | 2 |
| C17×#1721 | 2 |
| #19721 | 17 |