Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2810 conjugacy classes of subgroups.
The subgroup lattice has 298 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #20283283 | C2 | direct (N × H) |
| 3. C2×#16810650 | C2 | semidirect |
| 4. C2×#16810647 | C2 | semidirect |
| 5. C22×C4⋊#88322 | C2 | semidirect |
| 11. #16810650 | C22 | semidirect |
| 12. #16810647 | C22 | semidirect |
| 17. C2×C4⋊#88322 | C22 | semidirect |
| 113. C2×C4×C53 | #131 | semidirect |
| 141. C4×C53 | C2×#131 | semidirect |
| 151. C2×C53 | #2906 | semidirect |
| 175. C53 | C2×#2906 | semidirect |
| 262. C2×C4 | #13133224 | semidirect |
| 289. C4 | C2×#13133224 | semidirect |
| 293. C2 | #20283283 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133224 | 2 |
| #20283283 | 2 |
| C2×#16810650 | 2 |
| C2×#16810647 | 2 |
| C22×C4⋊#88322 | 2 |
| C2×C4×#41×C53 | 2 |
| C2×#2906 | 53 |