Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
310 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 2. #70945 | C2 | semidirect |
| 4. #69046 | C2 | semidirect |
| 5. C3×Q8⋊C16 | C2 | semidirect |
| 6. #67564 | C2 | semidirect |
| 31. Q8⋊C16 | D3 | semidirect |
| 244. C3 | #12408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D24 | 2 |
| #70945 | 2 |
| #69290 | 2 |
| #69046 | 2 |
| C3×Q8⋊C16 | 2 |
| #67564 | 2 |
| #67504 | 2 |
| #12408 | 3 |