Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
992 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 992 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 |
|---|---|---|
| 1. C2×D137⋊M16 | C2 | semidirect |
| 2. D137⋊#100 | C2 | direct (N × H) |
| 3. C2×#17984148 | C2 | semidirect |
| 7. D137⋊M16 | C22 | semidirect |
| 8. C2×#14555519 | C22 | semidirect |
| 10. #17984148 | C22 | semidirect |
| 23. #14555519 | C23 | semidirect |
| 108. C2×D137 | #100 | semidirect |
| 117. C2×C137 | C2×#100 | semidirect |
| 121. D137 | C2×#100 | semidirect |
| 122. C137 | C22×#100 | semidirect |
| 243. C2 | D137⋊#100 | 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 |
| D137⋊#100 | 2 |
| C2×#17984148 | 2 |
| C22×D4×D137 | 2 |
| C22×#100 | 137 |