Finite Group DatabasebetaFinite Group DatabasebetaOrder 17216.
120 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 49 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. Q8×Dic269 | C2 | semidirect |
| 4. #22575386 | C2 | semidirect |
| 6. #22575363 | C2 | semidirect |
| 7. #103×C269 | C2 | semidirect |
| 10. #16864389 | C4 | semidirect |
| 27. #14524130 | C2×C4 | semidirect |
| 29. Q8×C269 | C2×C4 | semidirect |
| 49. C269 | #440 | semidirect |
| 55. #103 | D269 | semidirect |
| 72. Q8 | C4×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16864389 | 2 |
| Q8×Dic269 | 2 |
| #22575415 | 2 |
| #22575386 | 2 |
| #22575375 | 2 |
| #22575363 | 2 |
| #103×C269 | 2 |
| #440 | 269 |