Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2638 conjugacy classes of subgroups.
The subgroup lattice has 304 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #20272977 | C2 | direct (N × H) |
| 12. C2×#95×C53 | C4 | semidirect |
| 37. #95×C53 | C2×C4 | semidirect |
| 148. C2×C53 | #1443 | semidirect |
| 163. C2×#95 | Dic53 | semidirect |
| 165. C53 | C2×#1443 | semidirect |
| 189. #95 | C2×Dic53 | semidirect |
| 295. C2 | #20272977 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133124 | 2 |
| #20272977 | 2 |
| C22×#95×C53 | 2 |
| C2×#1443 | 53 |