Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
240 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 240 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 |
|---|---|---|
| 1. #14531008 | C2 | semidirect |
| 2. C16×D68 | C2 | semidirect |
| 3. #14528174 | C2 | semidirect |
| 5. #14526840 | C2 | semidirect |
| 6. #14526829 | C2 | semidirect |
| 7. C17×#1371 | C2 | semidirect |
| 99. #1371 | D17 | semidirect |
| 157. C17 | #12467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14531008 | 2 |
| C16×D68 | 2 |
| #14528174 | 2 |
| #14528140 | 2 |
| #14526840 | 2 |
| #14526829 | 2 |
| C17×#1371 | 2 |
| #12467 | 17 |