Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
756 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 198 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. #22578481 | C2 | semidirect |
| 2. #22578390 | C2 | semidirect |
| 3. #22578389 | C2 | semidirect |
| 4. D137⋊#100 | C2 | semidirect |
| 5. C2×#17984148 | C2 | semidirect |
| 8. D137⋊M16 | C22 | semidirect |
| 9. C2×#14555519 | C22 | semidirect |
| 10. #17984149 | C22 | semidirect |
| 11. #17984148 | C22 | semidirect |
| 12. #17984148 | C22 | semidirect |
| 131. C137 | #2888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578481 | 2 |
| #22578390 | 2 |
| #22578389 | 2 |
| D137⋊#100 | 2 |
| C2×#17984148 | 2 |
| C2×#17984133 | 2 |
| #2888 | 137 |