Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
216 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 122 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 |
|---|---|---|
| 3. C16×#10587739 | C2 | direct (N × H) |
| 7. #17984161 | C4 | semidirect |
| 9. C2×#14555513 | C4 | semidirect |
| 13. C2×#14555485 | C4 | semidirect |
| 14. C16×D137 | C4 | semidirect |
| 16. C2×C16×C137 | C4 | semidirect |
| 23. #14555513 | C2×C4 | semidirect |
| 30. #14555485 | C2×C4 | semidirect |
| 32. C16×C137 | C2×C4 | semidirect |
| 33. C2×#10587739 | C16 | direct (N × H) |
| 51. #10587739 | C2×C16 | direct (N × H) |
| 56. C2×C137 | C4×C16 | semidirect |
| 58. D137 | C4×C16 | semidirect |
| 60. C137 | C2×C4×C16 | semidirect |
| 75. C2×C16 | #10587739 | direct (N × H) |
| 93. C16 | C2×#10587739 | direct (N × H) |
| 119. C2 | C16×#10587739 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984161 | 2 |
| C2×C8×#10587739 | 2 |
| C16×#10587739 | 2 |
| C2×C16×D137 | 2 |
| C2×C4×C16 | 137 |