Order 12032.
1454 conjugacy classes of subgroups.
The subgroup lattice has 356 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #20244716 | C2 | direct (N × H) |
| 32. C22×C47⋊C8 | Q8 | semidirect |
| 54. C2×C4⋊C4×C47 | Q8 | semidirect |
| 97. C4⋊C4×C47 | C2×Q8 | semidirect |
| 107. C2×C47⋊C8 | C2×Q8 | semidirect |
| 176. C2×C47 | #2057 | semidirect |
| 202. C47 | C2×#2057 | semidirect |
| 231. C2×C4⋊C4 | Dic94 | semidirect |
| 283. C4⋊C4 | C2×Dic94 | semidirect |
| 347. C2 | #20244716 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13094024 | 2 |
| C22×#13093957 | 2 |
| #20244716 | 2 |
| C2×#15688885 | 2 |
| C2×#15688878 | 2 |
| C2×C47×#389 | 2 |
| C2×#2057 | 47 |