Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
216 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 119 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. #10587739⋊C16 | C2 | direct (N × H) |
| 4. #17984183 | C4 | semidirect |
| 6. C2×#14555522 | C4 | semidirect |
| 12. #14555522 | C2×C4 | semidirect |
| 25. C2×#10587739 | C16 | semidirect |
| 42. #10587739 | C2×C16 | semidirect |
| 47. C2×C137 | C4×C16 | semidirect |
| 49. D137 | C4×C16 | semidirect |
| 51. C137 | C2×C4×C16 | semidirect |
| 101. C2 | #10587739⋊C16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984183 | 2 |
| #10587739⋊C16 | 2 |
| C2×C8×#10587739 | 2 |
| C2×C4×C16 | 137 |