Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
502 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 131 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×#16863829 | C2 | semidirect |
| 2. C2×D16×D67 | C2 | semidirect |
| 3. #22562523 | C2 | direct (N × H) |
| 4. C2×#16863233 | C2 | semidirect |
| 5. C2×D2144 | C2 | semidirect |
| 6. C2×#16863231 | C2 | semidirect |
| 7. C2×#16863229 | C2 | semidirect |
| 8. C2×SD64×C67 | C2 | semidirect |
| 12. #16863829 | C22 | semidirect |
| 15. C2×D1072 | C22 | semidirect |
| 18. D16×D67 | C22 | semidirect |
| 20. #16863233 | C22 | semidirect |
| 21. D2144 | C22 | semidirect |
| 22. #16863231 | C22 | semidirect |
| 23. #16863229 | C22 | semidirect |
| 24. C2×C67⋊C32 | C22 | semidirect |
| 25. C2×Q32×C67 | C22 | semidirect |
| 27. SD64×C67 | C22 | semidirect |
| 28. C2×C32×C67 | C22 | semidirect |
| 44. D1072 | C23 | semidirect |
| 49. C67⋊C32 | C23 | semidirect |
| 53. Q32×C67 | C23 | semidirect |
| 57. C32×C67 | C23 | semidirect |
| 129. C2×C67 | #2263 | semidirect |
| 138. C2×SD64 | D67 | semidirect |
| 142. C67 | C2×#2263 | semidirect |
| 147. C2×Q32 | C2×D67 | semidirect |
| 157. SD64 | C2×D67 | semidirect |
| 162. C2×C32 | C2×D67 | semidirect |
| 177. Q32 | C22×D67 | semidirect |
| 191. C32 | C22×D67 | semidirect |
| 265. C2 | #22562523 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863829 | 2 |
| C2×D16×D67 | 2 |
| #22562523 | 2 |
| C2×#16863233 | 2 |
| C2×D2144 | 2 |
| C2×#16863231 | 2 |
| C2×#16863229 | 2 |
| C2×SD64×C67 | 2 |
| C2×#2263 | 67 |