Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
3006 conjugacy classes of subgroups.
The subgroup lattice has 330 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#11718121 | C2 | direct (N × H) |
| 10. C22×C13×C4⋊C4 | C4 | semidirect |
| 14. C22×C4⋊Dic13 | C4 | semidirect |
| 18. C23×#1055 | C4 | semidirect |
| 20. #11718121 | C22 | direct (N × H) |
| 41. C2×C13×C4⋊C4 | C2×C4 | semidirect |
| 46. C2×C4⋊Dic13 | C2×C4 | semidirect |
| 51. C22×#1055 | C2×C4 | semidirect |
| 89. C13×C4⋊C4 | C22×C4 | semidirect |
| 92. C4⋊Dic13 | C22×C4 | semidirect |
| 96. C2×#1055 | C22×C4 | semidirect |
| 152. C22×C4⋊C4 | Dic13 | semidirect |
| 155. C22×C13 | #340 | semidirect |
| 207. C2×C4⋊C4 | C2×Dic13 | semidirect |
| 209. C2×C13 | C2×#340 | semidirect |
| 259. C4⋊C4 | C22×Dic13 | semidirect |
| 260. C13 | C22×#340 | semidirect |
| 299. C22 | #11718121 | direct (N × H) |
| 321. C2 | C2×#11718121 | 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 |
| C23×C4⋊Dic13 | 2 |
| C2×#11718121 | 2 |
| C23×C13×C4⋊C4 | 2 |
| C22×#340 | 13 |