Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
454 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 3. #14527257 | C2 | semidirect |
| 5. #14527140 | C2 | semidirect |
| 6. #14526656 | C2 | semidirect |
| 7. C17×#3166 | C2 | semidirect |
| 161. #3166 | D17 | semidirect |
| 263. C17 | #10126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539974 | 2 |
| #14539791 | 2 |
| #14527257 | 2 |
| #14527202 | 2 |
| #14527140 | 2 |
| #14526656 | 2 |
| C17×#3166 | 2 |
| #10126 | 17 |