Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
422 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 9. #11763212 | C4 | semidirect |
| 10. #11763188 | C4 | semidirect |
| 11. #11763161 | C4 | semidirect |
| 12. #11763159 | C4 | semidirect |
| 85. C42×C17 | Q16 | semidirect |
| 217. C17 | #9848 | semidirect |
| 255. C42 | #63231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539366 | 2 |
| #14529761 | 2 |
| #14528530 | 2 |
| #14527542 | 2 |
| #14527239 | 2 |
| #14527238 | 2 |
| C17×#1994 | 2 |
| #9848 | 17 |