Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
512 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 210 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. #22578410 | C2 | semidirect |
| 4. #22578409 | C2 | semidirect |
| 5. #22578404 | C2 | semidirect |
| 15. #17984155 | C22 | semidirect |
| 16. C4⋊#11764047 | C22 | semidirect |
| 95. D137 | #424 | semidirect |
| 96. C137 | C2×#424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D137⋊M16 | 2 |
| C22×#14555518 | 2 |
| #22578410 | 2 |
| #22578409 | 2 |
| #22578404 | 2 |
| #117×D137 | 2 |
| C2×#424 | 137 |