Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
428 conjugacy classes of subgroups.
The subgroup lattice has 330 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #20272709 | C2 | direct (N × H) |
| 167. C2×C53 | #1342 | semidirect |
| 184. C53 | C2×#1342 | semidirect |
| 327. C2 | #20272709 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810405 | 2 |
| C2×#16810381 | 2 |
| #20272709 | 2 |
| C2×C53×#470 | 2 |
| C2×#1342 | 53 |