Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
714 conjugacy classes of subgroups.
The subgroup lattice has 354 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #20272538 | C2 | direct (N × H) |
| 41. C2×C4⋊C4×C53 | C8 | semidirect |
| 85. C4⋊C4×C53 | C2×C8 | semidirect |
| 173. C2×C53 | #1271 | semidirect |
| 196. C53 | C2×#1271 | semidirect |
| 218. C2×C4⋊C4 | #88322 | semidirect |
| 270. C4⋊C4 | C2×#88322 | semidirect |
| 345. C2 | #20272538 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810378 | 2 |
| #20272538 | 2 |
| C2×C53×#389 | 2 |
| C2×#1271 | 53 |