Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
458 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 95 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. C2×C3×#349 | C2 | semidirect |
| 3. #72000 | C2 | semidirect |
| 4. C2×#4516 | C2 | semidirect |
| 5. C2×#4516 | C2 | semidirect |
| 6. C2×#4513 | C2 | semidirect |
| 7. #67816 | C2 | semidirect |
| 30. C2×#349 | D3 | semidirect |
| 59. C3×M32 | D4 | semidirect |
| 160. M32 | #67 | semidirect |
| 336. C3 | #13398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5135 | 2 |
| C2×C3×#349 | 2 |
| #72000 | 2 |
| C2×#4516 | 2 |
| C2×#4513 | 2 |
| #67816 | 2 |
| #13398 | 3 |