Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
386 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 93 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. #72081 | C2 | semidirect |
| 3. C2×#4567 | C2 | semidirect |
| 4. #72014 | C2 | semidirect |
| 5. C2×#4561 | C2 | semidirect |
| 6. C2×#4493 | C2 | semidirect |
| 7. #67731 | C2 | semidirect |
| 342. C3 | #13392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3067 | 2 |
| #72081 | 2 |
| C2×#4567 | 2 |
| #72014 | 2 |
| C2×#4561 | 2 |
| C2×#4493 | 2 |
| #67731 | 2 |
| #13392 | 3 |