Order 12032.
1554 conjugacy classes of subgroups.
The subgroup lattice has 370 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #20243496 | C2 | direct (N × H) |
| 3. C2×#15688889 | C2 | semidirect |
| 9. #15688889 | C22 | semidirect |
| 12. C47×#518 | C4 | semidirect |
| 15. C2×#117×C47 | C4 | semidirect |
| 16. C22×C22⋊C4×C47 | C4 | semidirect |
| 40. #117×C47 | C2×C4 | semidirect |
| 49. C2×C22⋊C4×C47 | C2×C4 | semidirect |
| 187. C2×C47 | #1828 | semidirect |
| 191. #518 | Dic47 | semidirect |
| 194. C2×#117 | Dic47 | semidirect |
| 196. C22×C22⋊C4 | Dic47 | semidirect |
| 202. C47 | C2×#1828 | semidirect |
| 218. #117 | C2×Dic47 | semidirect |
| 233. C2×C22⋊C4 | C2×Dic47 | semidirect |
| 367. C2 | #20243496 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13093939 | 2 |
| #20243496 | 2 |
| C2×#15688889 | 2 |
| C2×C47×#518 | 2 |
| C2×#1828 | 47 |