Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
232 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 59 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. C2×#11762644 | C2 | semidirect |
| 2. #14531032 | C2 | semidirect |
| 3. D16×Dic17 | C2 | semidirect |
| 4. #14526979 | C2 | semidirect |
| 5. #14526963 | C2 | semidirect |
| 6. #14526962 | C2 | semidirect |
| 7. C2×C17×D32 | C2 | semidirect |
| 30. C17×D16 | D4 | semidirect |
| 83. C2×D32 | D17 | semidirect |
| 103. Dic17 | D32 | semidirect |
| 135. D16 | C22⋊D17 | semidirect |
| 143. C17 | #13685 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11762644 | 2 |
| #14531032 | 2 |
| D16×Dic17 | 2 |
| #14526979 | 2 |
| #14526963 | 2 |
| #14526962 | 2 |
| C2×C17×D32 | 2 |
| #13685 | 17 |