Order 13568.
1198 conjugacy classes of subgroups.
The subgroup lattice has 394 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #20290886 | C2 | semidirect |
| 4. #20290885 | C2 | semidirect |
| 5. #20290884 | C2 | semidirect |
| 35. C22×#88324 | Q8 | semidirect |
| 227. C53 | #21300 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811626 | 2 |
| C22×C4×#88324 | 2 |
| #20290886 | 2 |
| #20290885 | 2 |
| #20290884 | 2 |
| #20290381 | 2 |
| C2×#16811175 | 2 |
| #21300 | 53 |