Order 13568.
1342 conjugacy classes of subgroups.
The subgroup lattice has 388 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 24. C53×#376 | C4 | semidirect |
| 104. C42×C53 | C4⋊C4 | semidirect |
| 209. #376 | Dic53 | semidirect |
| 221. C53 | #13952 | semidirect |
| 301. C42 | C4⋊Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810491 | 2 |
| C2×C4×C4⋊Dic53 | 2 |
| #20272980 | 2 |
| #20272972 | 2 |
| #20272949 | 2 |
| #20272945 | 2 |
| #20272942 | 2 |
| C2×C53×#376 | 2 |
| #13952 | 53 |