Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
220 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 65 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×#4449 | C2 | semidirect |
| 2. C4×Dic24 | C2 | semidirect |
| 4. C3×C4⋊C32 | C2 | semidirect |
| 5. #67596 | C2 | semidirect |
| 20. C4⋊C32 | D3 | semidirect |
| 33. Dic24 | D4 | semidirect |
| 120. C3×C4 | SD64 | semidirect |
| 151. C4 | #4449 | semidirect |
| 154. C3 | #13686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4449 | 2 |
| C4×Dic24 | 2 |
| #69060 | 2 |
| C3×C4⋊C32 | 2 |
| #67596 | 2 |
| #13686 | 3 |