Order 3328.
2046 conjugacy classes of subgroups.
The subgroup lattice has 322 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C22×C4×#1055 | C2 | semidirect |
| 4. C22⋊C4×#1055 | C2 | direct (N × H) |
| 5. C2×#11718116 | C2 | semidirect |
| 11. C23×#1055 | C4 | semidirect |
| 19. C2×C22⋊#1055 | C4 | semidirect |
| 22. C2×C4×#1055 | C22 | semidirect |
| 23. #11718116 | C22 | semidirect |
| 34. C2×C13×C22⋊C4 | C8 | semidirect |
| 48. C22×#1055 | C2×C4 | semidirect |
| 54. C22⋊#1055 | C2×C4 | semidirect |
| 74. C22×C4×C13 | C2×C8 | semidirect |
| 85. C13×C22⋊C4 | C2×C8 | semidirect |
| 95. C2×#1055 | C22⋊C4 | direct (N × H) |
| 111. C23×C13 | C4×C8 | semidirect |
| 134. C2×C4×C13 | C22×C8 | semidirect |
| 141. #1055 | C2×C22⋊C4 | direct (N × H) |
| 165. C22×C13 | C2×C4×C8 | semidirect |
| 201. C2×C22⋊C4 | #1055 | direct (N × H) |
| 211. C2×C13 | C8×C22⋊C4 | semidirect |
| 231. C22×C4 | C2×#1055 | semidirect |
| 255. C22⋊C4 | C2×#1055 | direct (N × H) |
| 259. C13 | C2×C8×C22⋊C4 | semidirect |
| 265. C23 | C4×#1055 | semidirect |
| 285. C2×C4 | C22×#1055 | semidirect |
| 301. C22 | C2×C4×#1055 | semidirect |
| 316. C2 | C22⋊C4×#1055 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#1055 | 2 |
| C22×C22⋊#1055 | 2 |
| C22×C4×#1055 | 2 |
| C22⋊C4×#1055 | 2 |
| C2×#11718116 | 2 |
| C2×C4×C13×C22⋊C4 | 2 |
| C2×C8×C22⋊C4 | 13 |