Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
470 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 470 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×#16811056 | C2 | semidirect |
| 2. C2×#16811052 | C2 | semidirect |
| 3. #20277023 | C2 | direct (N × H) |
| 4. C2×#16810463 | C2 | semidirect |
| 5. C2×#16810462 | C2 | semidirect |
| 6. C2×#16810458 | C2 | semidirect |
| 7. C2×C32×D53 | C2 | semidirect |
| 8. C2×C53×SD64 | C2 | semidirect |
| 12. #16811056 | C22 | semidirect |
| 14. #16811052 | C22 | semidirect |
| 20. #16810463 | C22 | semidirect |
| 21. #16810462 | C22 | semidirect |
| 22. #16810458 | C22 | semidirect |
| 24. C32×D53 | C22 | semidirect |
| 27. C53×SD64 | C22 | semidirect |
| 130. C2×SD64 | D53 | semidirect |
| 134. C2×C53 | #2262 | semidirect |
| 153. SD64 | C2×D53 | semidirect |
| 158. C53 | C2×#2262 | semidirect |
| 257. C2 | #20277023 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811056 | 2 |
| C2×#16811052 | 2 |
| #20277023 | 2 |
| C2×#16810463 | 2 |
| C2×#16810462 | 2 |
| C2×#16810458 | 2 |
| C2×C32×D53 | 2 |
| C2×C53×SD64 | 2 |
| C2×#2262 | 53 |