Finite Group DatabasebetaFinite Group DatabasebetaOrder 17216.
162 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 2. C2×C4⋊Dic269 | C2 | semidirect |
| 3. #22575378 | C2 | semidirect |
| 4. #22575375 | C2 | semidirect |
| 5. C2×M16×C269 | C2 | semidirect |
| 7. #16864402 | C4 | semidirect |
| 20. Dic538 | C2×C4 | semidirect |
| 22. D1076 | C2×C4 | semidirect |
| 51. C269 | #417 | semidirect |
| 54. C2×M16 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16864402 | 2 |
| C2×C4⋊Dic269 | 2 |
| #22575378 | 2 |
| #22575375 | 2 |
| C2×M16×C269 | 2 |
| #417 | 269 |