Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
202 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 75 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. Q32×Dic13 | C2 | semidirect |
| 3. #13113038 | C2 | semidirect |
| 4. #13113017 | C2 | semidirect |
| 6. C32×Dic13 | C2 | semidirect |
| 12. C13×SD64 | C4 | semidirect |
| 25. C13×Q32 | C2×C4 | semidirect |
| 35. C13×C32 | C2×C4 | semidirect |
| 82. SD64 | Dic13 | direct (N × H) |
| 100. Dic13 | SD64 | direct (N × H) |
| 106. Q32 | C2×Dic13 | semidirect |
| 117. C32 | C2×Dic13 | semidirect |
| 140. C13 | C4×SD64 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q32×Dic13 | 2 |
| D16×Dic13 | 2 |
| #13113038 | 2 |
| #13113017 | 2 |
| #13113014 | 2 |
| C32×Dic13 | 2 |
| C2×C13×SD64 | 2 |
| C4×SD64 | 13 |