Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
554 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 125 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. #14529612 | C2 | semidirect |
| 3. C42×#3622 | C2 | semidirect |
| 4. #14527542 | C2 | semidirect |
| 5. #14527235 | C2 | semidirect |
| 6. #14527234 | C2 | semidirect |
| 7. C17×#1962 | C2 | semidirect |
| 9. #11763212 | C4 | semidirect |
| 10. #11763185 | C4 | semidirect |
| 11. #11763157 | C4 | semidirect |
| 12. #11763155 | C4 | semidirect |
| 96. C42×C17 | D8 | semidirect |
| 150. #3622 | #104 | semidirect |
| 153. #1962 | D17 | semidirect |
| 243. C17 | #9844 | semidirect |
| 285. C42 | #63228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539359 | 2 |
| #14529612 | 2 |
| C42×#3622 | 2 |
| #14527542 | 2 |
| #14527235 | 2 |
| #14527234 | 2 |
| C17×#1962 | 2 |
| #9844 | 17 |