Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2110 conjugacy classes of subgroups.
The subgroup lattice has 492 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #20274441 | C2 | direct (N × H) |
| 4. C2×#16810387 | C2 | semidirect |
| 20. #16810387 | C22 | semidirect |
| 248. C2×C53 | #1738 | semidirect |
| 274. C53 | C2×#1738 | semidirect |
| 488. C2 | #20274441 | 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 |
| #20274441 | 2 |
| C2×#16810387 | 2 |
| C23×M16×C53 | 2 |
| C2×#1738 | 53 |