Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
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×#16811052 | C2 | semidirect |
| 2. C2×D16×D53 | C2 | semidirect |
| 3. #20277026 | C2 | direct (N × H) |
| 4. C2×#16810462 | C2 | semidirect |
| 5. C2×#16810461 | C2 | semidirect |
| 6. C2×#16810458 | C2 | semidirect |
| 7. C2×#16810456 | C2 | semidirect |
| 8. C2×C53×D32 | C2 | semidirect |
| 12. #16811052 | C22 | semidirect |
| 13. C2×Dic424 | C22 | semidirect |
| 18. D16×D53 | C22 | semidirect |
| 20. #16810462 | C22 | semidirect |
| 21. #16810461 | C22 | semidirect |
| 22. #16810458 | C22 | semidirect |
| 23. #16810456 | C22 | semidirect |
| 24. C2×#13133123 | C22 | semidirect |
| 26. C2×D16×C53 | C22 | semidirect |
| 27. C53×D32 | C22 | semidirect |
| 28. C2×C32×C53 | C22 | semidirect |
| 41. Dic424 | C23 | semidirect |
| 49. #13133123 | C23 | semidirect |
| 55. D16×C53 | C23 | semidirect |
| 57. C32×C53 | C23 | semidirect |
| 134. C2×D32 | D53 | semidirect |
| 138. C2×C53 | #2263 | semidirect |
| 153. C2×D16 | C2×D53 | semidirect |
| 158. D32 | C2×D53 | semidirect |
| 161. C2×C32 | C2×D53 | semidirect |
| 162. C53 | C2×#2263 | semidirect |
| 185. D16 | C22×D53 | semidirect |
| 191. C32 | C22×D53 | semidirect |
| 265. C2 | #20277026 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811052 | 2 |
| C2×D16×D53 | 2 |
| #20277026 | 2 |
| C2×#16810462 | 2 |
| C2×#16810461 | 2 |
| C2×#16810458 | 2 |
| C2×#16810456 | 2 |
| C2×C53×D32 | 2 |
| C2×#2263 | 53 |