Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
756 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 202 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. C2×D137⋊M16 | C2 | semidirect |
| 2. #22578389 | C2 | direct (N × H) |
| 3. C2×#17984149 | C2 | semidirect |
| 4. C2×#17984148 | C2 | semidirect |
| 8. D137⋊M16 | C22 | semidirect |
| 11. #17984149 | C22 | semidirect |
| 12. #17984148 | C22 | semidirect |
| 135. C2×C137 | #413 | semidirect |
| 139. C137 | C2×#413 | semidirect |
| 277. C2 | #22578389 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D137⋊M16 | 2 |
| #22578389 | 2 |
| C2×#17984149 | 2 |
| C2×#17984148 | 2 |
| C22×#14555510 | 2 |
| C2×#413 | 137 |