Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
212 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 67 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. #70906 | C2 | semidirect |
| 4. C3×#1334 | C2 | semidirect |
| 6. #67512 | C2 | semidirect |
| 7. #67464 | C2 | semidirect |
| 28. #1334 | D3 | semidirect |
| 89. C3⋊C16 | M16 | semidirect |
| 200. C3 | #12087 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #70913 | 2 |
| #70906 | 2 |
| #68525 | 2 |
| C3×#1334 | 2 |
| #67516 | 2 |
| #67512 | 2 |
| #67464 | 2 |
| #12087 | 3 |