Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1870 conjugacy classes of subgroups; only the 256 normal subgroups are shown.
This group has 1870 conjugacy classes of subgroups — too many to draw. Only its 256 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#11719128 | C2 | semidirect |
| 2. #13130363 | C2 | direct (N × H) |
| 3. C2×#11718297 | C2 | semidirect |
| 17. #11719128 | C22 | semidirect |
| 18. C2×#88112 | C22 | semidirect |
| 20. #11718297 | C22 | semidirect |
| 56. #88112 | C23 | semidirect |
| 227. C2×C13 | #1555 | semidirect |
| 280. C13 | C2×#1555 | semidirect |
| 344. C2 | #13130363 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11719128 | 2 |
| #13130363 | 2 |
| C2×#11718297 | 2 |
| C22×#88194 | 2 |
| C2×#1555 | 13 |