Order 13568.
914 conjugacy classes of subgroups.
The subgroup lattice has 380 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #20289920 | C2 | semidirect |
| 4. #20289916 | C2 | semidirect |
| 5. C8×#11719940 | C2 | semidirect |
| 21. #88324⋊C8 | C22 | semidirect |
| 22. C8×#88324 | C22 | semidirect |
| 32. C2×#11719940 | C8 | semidirect |
| 94. #11719940 | C2×C8 | semidirect |
| 95. #11719940 | C2×C8 | semidirect |
| 97. C2×#88324 | C2×C8 | semidirect |
| 221. C53 | #17314 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811640 | 2 |
| C2×C4×#11719940 | 2 |
| #20289920 | 2 |
| #20289916 | 2 |
| C8×#11719940 | 2 |
| C2×#16810673 | 2 |
| #17314 | 53 |