Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
310 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 3. #71385 | C2 | semidirect |
| 4. #71378 | C2 | semidirect |
| 6. #67564 | C2 | semidirect |
| 7. #67558 | C2 | semidirect |
| 244. C3 | #12408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×Dic6 | 2 |
| C3×#2226 | 2 |
| #71385 | 2 |
| #71378 | 2 |
| #67763 | 2 |
| #67564 | 2 |
| #67558 | 2 |
| #12408 | 3 |