Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
930 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 219 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. C22×#13133160 | C2 | semidirect |
| 2. C22×#13133158 | C2 | semidirect |
| 3. C2×#16811000 | C2 | semidirect |
| 4. #20276982 | C2 | direct (N × H) |
| 5. C2×#16810399 | C2 | semidirect |
| 6. C2×C53×#495 | C2 | semidirect |
| 11. C2×#13133160 | C22 | semidirect |
| 13. C2×#13133158 | C22 | semidirect |
| 16. #16811000 | C22 | semidirect |
| 17. #16810399 | C22 | semidirect |
| 23. C53×#495 | C22 | semidirect |
| 37. C2×#11719908 | D4 | semidirect |
| 93. #11719908 | C2×D4 | semidirect |
| 139. C2×#495 | D53 | semidirect |
| 144. C2×C53 | #2250 | semidirect |
| 161. #495 | C2×D53 | semidirect |
| 166. C53 | C2×#2250 | semidirect |
| 280. C2 | #20276982 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133160 | 2 |
| C22×#13133158 | 2 |
| C2×#16811000 | 2 |
| #20276982 | 2 |
| C2×#16810399 | 2 |
| C2×C53×#495 | 2 |
| C2×#2250 | 53 |