Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
428 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 428 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×#350 | C2 | semidirect |
| 3. #72016 | C2 | semidirect |
| 4. C2×#4516 | C2 | semidirect |
| 5. #71428 | C2 | semidirect |
| 6. C2×#4509 | C2 | semidirect |
| 7. #67807 | C2 | semidirect |
| 32. C2×#350 | D3 | semidirect |
| 60. C3×M32 | D4 | semidirect |
| 169. M32 | #67 | semidirect |
| 359. C3 | #13387 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83799 | 2 |
| C2×C3×#350 | 2 |
| #72016 | 2 |
| C2×#4516 | 2 |
| #71428 | 2 |
| C2×#4509 | 2 |
| #67807 | 2 |
| #13387 | 3 |