Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
288 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 4. #14526842 | C2 | semidirect |
| 5. #14526840 | C2 | semidirect |
| 6. #14526838 | C2 | semidirect |
| 7. C17×#1365 | C2 | semidirect |
| 109. #1365 | D17 | semidirect |
| 174. C17 | #11973 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539295 | 2 |
| #14530582 | 2 |
| #14527546 | 2 |
| #14526842 | 2 |
| #14526840 | 2 |
| #14526838 | 2 |
| C17×#1365 | 2 |
| #11973 | 17 |