Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
360 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 85 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. #69073 | C2 | semidirect |
| 3. #68530 | C2 | semidirect |
| 4. C3×#1334 | C2 | semidirect |
| 5. #67764 | C2 | semidirect |
| 6. #67516 | C2 | semidirect |
| 7. #67465 | C2 | semidirect |
| 32. #1334 | D3 | semidirect |
| 305. C3 | #11665 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#919 | 2 |
| #69073 | 2 |
| #68530 | 2 |
| C3×#1334 | 2 |
| #67764 | 2 |
| #67516 | 2 |
| #67465 | 2 |
| #11665 | 3 |