Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
5294 conjugacy classes of subgroups; only the 827 normal subgroups are shown.
This group has 5294 conjugacy classes of subgroups — too many to draw. Only its 827 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×#88189 | C2 | semidirect |
| 2. C2×#11718904 | C2 | direct (N × H) |
| 3. C22×#88074 | C2 | semidirect |
| 10. C24×Dic13 | C22 | semidirect |
| 12. C22×C22⋊Dic13 | C22 | semidirect |
| 14. C2×#88189 | C22 | semidirect |
| 16. #11718904 | C22 | direct (N × H) |
| 17. C2×#88074 | C22 | semidirect |
| 39. C23×Dic13 | C23 | semidirect |
| 42. C2×C22⋊Dic13 | C23 | semidirect |
| 44. #88189 | C23 | semidirect |
| 46. #88074 | C23 | semidirect |
| 81. C22×Dic13 | C24 | semidirect |
| 84. C22⋊Dic13 | C24 | semidirect |
| 143. C22×C13 | #458 | semidirect |
| 182. C2×C13 | C2×#458 | semidirect |
| 222. C13 | C22×#458 | semidirect |
| 263. C22 | #11718904 | direct (N × H) |
| 273. C2 | C2×#11718904 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#88189 | 2 |
| C2×#11718904 | 2 |
| C22×#88074 | 2 |
| C22×C13×H(5,𝔽2) | 2 |
| C22×#458 | 13 |