Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
604 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 105 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. C3×#3078 | C2 | semidirect |
| 4. #71835 | C2 | semidirect |
| 5. #71621 | C2 | semidirect |
| 7. #67715 | C2 | semidirect |
| 33. #3078 | D3 | semidirect |
| 116. C2×C3×Q8 | SD16 | semidirect |
| 263. C2×Q8 | #215 | semidirect |
| 408. C3 | #10250 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3078 | 2 |
| #83355 | 2 |
| #82476 | 2 |
| #71835 | 2 |
| #71621 | 2 |
| #70502 | 2 |
| #67715 | 2 |
| #10250 | 3 |