Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
492 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 2. #14529760 | C2 | semidirect |
| 4. C4×#10587486 | C2 | semidirect |
| 5. #14527238 | C2 | semidirect |
| 7. C17×#1567 | C2 | semidirect |
| 10. #11763207 | C4 | semidirect |
| 11. #11763182 | C4 | semidirect |
| 12. #11763160 | C4 | semidirect |
| 13. #11763156 | C4 | semidirect |
| 141. C8×C17 | #104 | semidirect |
| 147. #1567 | D17 | semidirect |
| 231. C17 | #9851 | semidirect |
| 307. C8 | #10587496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539343 | 2 |
| #14529760 | 2 |
| #14529611 | 2 |
| C4×#10587486 | 2 |
| #14527238 | 2 |
| #14527234 | 2 |
| C17×#1567 | 2 |
| #9851 | 17 |