Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
502 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 139 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×Q32×D53 | C2 | semidirect |
| 3. C2×#16810462 | C2 | semidirect |
| 4. C2×#16810461 | C2 | semidirect |
| 5. C2×#16810460 | C2 | semidirect |
| 6. SD64×D53 | C2 | direct (N × H) |
| 7. C2×C32×D53 | C2 | semidirect |
| 8. C2×C53×SD64 | C2 | semidirect |
| 11. C2×Dic424 | C22 | semidirect |
| 14. Q32×D53 | C22 | semidirect |
| 20. #16810462 | C22 | semidirect |
| 21. #16810461 | C22 | semidirect |
| 22. #16810460 | C22 | semidirect |
| 23. C2×#13133123 | C22 | semidirect |
| 24. C32×D53 | C22 | semidirect |
| 25. C2×Q32×C53 | C22 | semidirect |
| 27. C53×SD64 | C22 | semidirect |
| 28. C2×C32×C53 | C22 | semidirect |
| 41. Dic424 | C23 | semidirect |
| 49. #13133123 | C23 | semidirect |
| 53. Q32×C53 | C23 | semidirect |
| 57. C32×C53 | C23 | semidirect |
| 120. C2×D53 | SD64 | direct (N × H) |
| 133. C2×SD64 | D53 | direct (N × H) |
| 136. C2×C53 | C2×SD64 | semidirect |
| 139. D53 | C2×SD64 | direct (N × H) |
| 146. C2×Q32 | C2×D53 | semidirect |
| 156. SD64 | C2×D53 | direct (N × H) |
| 159. C2×C32 | C2×D53 | semidirect |
| 160. C53 | C22×SD64 | semidirect |
| 178. Q32 | C22×D53 | semidirect |
| 189. C32 | C22×D53 | semidirect |
| 261. C2 | SD64×D53 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q32×D53 | 2 |
| C2×D16×D53 | 2 |
| C2×#16810462 | 2 |
| C2×#16810461 | 2 |
| C2×#16810460 | 2 |
| SD64×D53 | 2 |
| C2×C32×D53 | 2 |
| C2×C53×SD64 | 2 |
| C22×SD64 | 53 |