Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
348 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 2. C2×#17984142 | C2 | semidirect |
| 3. C2×C8×#10587739 | C2 | semidirect |
| 5. #22578268 | C2 | semidirect |
| 6. #22578268 | C2 | semidirect |
| 8. C2×#14555520 | C4 | semidirect |
| 11. C2×#14555519 | C4 | semidirect |
| 23. C22⋊#11764040 | C4 | semidirect |
| 24. #17984000 | C4 | semidirect |
| 25. #17984000 | C4 | semidirect |
| 26. C22⋊C8×C137 | C4 | semidirect |
| 66. C2×#10587739 | M16 | semidirect |
| 68. #11764047 | C22⋊C4 | semidirect |
| 126. C137 | #1753 | semidirect |
| 150. C22⋊C8 | #10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D137⋊M16 | 2 |
| C2×#17984142 | 2 |
| C2×C8×#10587739 | 2 |
| C4×C22⋊#10587739 | 2 |
| #22578268 | 2 |
| C22⋊C8×D137 | 2 |
| #1753 | 137 |