Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
764 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 764 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. C22×#14555519 | C2 | semidirect |
| 2. #22578376 | C2 | semidirect |
| 3. #22578375 | C2 | semidirect |
| 4. #22578373 | C2 | semidirect |
| 8. C2×#14555519 | C22 | semidirect |
| 9. C22×#11764047 | C22 | semidirect |
| 10. #17984145 | C22 | semidirect |
| 11. C22⋊#11764047 | C22 | semidirect |
| 107. C137 | #2879 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555519 | 2 |
| #22578376 | 2 |
| #22578375 | 2 |
| #22578373 | 2 |
| C22×#14555509 | 2 |
| #2879 | 137 |