Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
224 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 65 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. #14526858 | C2 | semidirect |
| 5. #14526839 | C2 | semidirect |
| 6. #14526833 | C2 | semidirect |
| 7. C17×#2241 | C2 | semidirect |
| 91. #2241 | D17 | semidirect |
| 150. C17 | #12470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×D68 | 2 |
| #14528170 | 2 |
| #14528146 | 2 |
| #14526858 | 2 |
| #14526839 | 2 |
| #14526833 | 2 |
| C17×#2241 | 2 |
| #12470 | 17 |