Finite Group DatabasebetaFinite Group DatabasebetaOrder 17216.
246 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 111 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. #22575446 | C2 | direct (N × H) |
| 2. C2×C4⋊Dic269 | C2 | semidirect |
| 3. C2×#16864381 | C2 | semidirect |
| 4. C2×#16864381 | C2 | semidirect |
| 7. C2×C4×Dic269 | C2 | semidirect |
| 13. C4⋊Dic269 | C22 | semidirect |
| 14. #16864381 | C22 | semidirect |
| 15. #16864381 | C22 | semidirect |
| 18. C4×Dic269 | C22 | semidirect |
| 55. C2×C269 | #126 | semidirect |
| 59. C269 | C2×#126 | semidirect |
| 115. C2 | #22575446 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22575446 | 2 |
| C2×C4⋊Dic269 | 2 |
| C2×#16864381 | 2 |
| C2×C22⋊Dic269 | 2 |
| C2×C4×Dic269 | 2 |
| C2×C22⋊C4×C269 | 2 |
| C2×#126 | 269 |