Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
2022 conjugacy classes of subgroups; only the 400 normal subgroups are shown.
This group has 2022 conjugacy classes of subgroups — too many to draw. Only its 400 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. C22×#88112 | C2 | semidirect |
| 2. C2×#11718297 | C2 | direct (N × H) |
| 13. C2×#88112 | C22 | semidirect |
| 14. #11718297 | C22 | direct (N × H) |
| 39. #88112 | C23 | semidirect |
| 119. C22×C13 | #331 | semidirect |
| 157. C2×C13 | C2×#331 | semidirect |
| 194. C13 | C22×#331 | semidirect |
| 229. C22 | #11718297 | direct (N × H) |
| 240. C2 | C2×#11718297 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#88112 | 2 |
| C2×#11718297 | 2 |
| C22×#88194 | 2 |
| C22×#331 | 13 |