Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
3550 conjugacy classes of subgroups.
The subgroup lattice has 276 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #20272980 | C2 | direct (N × H) |
| 13. C2×#95×C53 | C4 | semidirect |
| 36. #95×C53 | C2×C4 | semidirect |
| 51. C22×C4×C53 | C4⋊C4 | semidirect |
| 96. C2×C4×C53 | C2×C4⋊C4 | semidirect |
| 134. C2×C53 | #1444 | semidirect |
| 150. C2×#95 | Dic53 | semidirect |
| 152. C53 | C2×#1444 | semidirect |
| 174. #95 | C2×Dic53 | semidirect |
| 205. C22×C4 | C4⋊Dic53 | semidirect |
| 244. C2×C4 | C2×C4⋊Dic53 | semidirect |
| 267. C2 | #20272980 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4⋊Dic53 | 2 |
| C22×#13133124 | 2 |
| #20272980 | 2 |
| C22×#95×C53 | 2 |
| C2×#1444 | 53 |