Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
566 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 167 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. #22562423 | C2 | semidirect |
| 3. #22561983 | C2 | semidirect |
| 4. C2×#16863208 | C2 | semidirect |
| 5. #22561830 | C2 | semidirect |
| 6. C67×#2916 | C2 | semidirect |
| 14. #16863220 | C22 | semidirect |
| 16. #16863178 | C22 | semidirect |
| 20. #430×C67 | C22 | semidirect |
| 132. #2916 | D67 | semidirect |
| 137. C67 | #33657 | semidirect |
| 146. #430 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569857 | 2 |
| #22562423 | 2 |
| #22561983 | 2 |
| C2×#16863208 | 2 |
| #22561830 | 2 |
| C67×#2916 | 2 |
| #33657 | 67 |