Order 13568.
1646 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 |
|---|---|---|
| 2. C2×#16811497 | C2 | semidirect |
| 7. #16811565 | C4 | semidirect |
| 11. C23×#88322 | C4 | semidirect |
| 14. C22×C8×D53 | C4 | semidirect |
| 16. C23×C8×C53 | C4 | semidirect |
| 96. C2×C8×C53 | C22⋊C4 | semidirect |
| 100. C2×#88322 | C22⋊C4 | semidirect |
| 161. C22×C53 | #340 | semidirect |
| 173. C2×D53 | #340 | semidirect |
| 206. C23×C8 | #6157 | semidirect |
| 213. C53 | #10721 | semidirect |
| 295. C2×C8 | C22⋊#6157 | semidirect |
| 371. C22 | #16811497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811565 | 2 |
| C2×#16811497 | 2 |
| C23×C8×D53 | 2 |
| #10721 | 53 |