Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
318 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 47. C2×C3×C16 | Q8 | semidirect |
| 53. #819 | Q8 | semidirect |
| 60. #812 | Q8 | semidirect |
| 133. C2×C16 | Dic6 | semidirect |
| 261. C3 | #13456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79139 | 2 |
| C2×C3×#367 | 2 |
| #70625 | 2 |
| #70596 | 2 |
| #67807 | 2 |
| #67805 | 2 |
| #67723 | 2 |
| #13456 | 3 |