Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
212 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 73 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. D16×Dic17 | C2 | semidirect |
| 2. #14526986 | C2 | semidirect |
| 3. #14526962 | C2 | semidirect |
| 4. #14526917 | C2 | semidirect |
| 12. C17×D32 | C4 | semidirect |
| 17. C17×D16 | C2×C4 | semidirect |
| 23. C17×C32 | C2×C4 | semidirect |
| 63. D32 | Dic17 | semidirect |
| 75. D16 | C2×Dic17 | semidirect |
| 82. C32 | C2×Dic17 | semidirect |
| 83. C17 | #13654 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D16×Dic17 | 2 |
| #14526986 | 2 |
| #14526962 | 2 |
| #14526917 | 2 |
| C2×C17×D32 | 2 |
| #13654 | 17 |