Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
306 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 1. #14541215 | C2 | semidirect |
| 2. #14531008 | C2 | semidirect |
| 3. #14530825 | C2 | semidirect |
| 5. #14526838 | C2 | semidirect |
| 6. #14526749 | C2 | semidirect |
| 7. C17×D4⋊C16 | C2 | semidirect |
| 120. D4⋊C16 | D17 | semidirect |
| 187. C17 | #12341 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14541215 | 2 |
| #14531008 | 2 |
| #14530825 | 2 |
| #14528139 | 2 |
| #14526838 | 2 |
| #14526749 | 2 |
| C17×D4⋊C16 | 2 |
| #12341 | 17 |