Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2830 conjugacy classes of subgroups.
The subgroup lattice has 280 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #20283279 | C2 | direct (N × H) |
| 3. C2×#16810650 | C2 | semidirect |
| 4. C2×#16810647 | C2 | semidirect |
| 11. #16810650 | C22 | semidirect |
| 12. #16810647 | C22 | semidirect |
| 13. C2×C4⋊#88322 | C22 | semidirect |
| 30. C4⋊#88322 | C23 | semidirect |
| 142. C2×C53 | #2905 | semidirect |
| 161. C53 | C2×#2905 | semidirect |
| 276. C2 | #20283279 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11719917 | 2 |
| #20283279 | 2 |
| C2×#16810650 | 2 |
| C2×#16810647 | 2 |
| C22×#117×C53 | 2 |
| C2×#2905 | 53 |