Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
504 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 147 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. C3×#2247 | C2 | semidirect |
| 4. #71496 | C2 | semidirect |
| 5. #71310 | C2 | semidirect |
| 7. #69046 | C2 | semidirect |
| 27. #2247 | D3 | semidirect |
| 205. C3 | #33749 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #81792 | 2 |
| C3×#2247 | 2 |
| #71505 | 2 |
| #71496 | 2 |
| #71310 | 2 |
| C4×#798 | 2 |
| #69046 | 2 |
| #33749 | 3 |