Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
566 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 167 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. #83789 | C2 | semidirect |
| 3. C3×#2115 | C2 | semidirect |
| 4. C2×#4516 | C2 | semidirect |
| 5. #71427 | C2 | semidirect |
| 6. #69116 | C2 | semidirect |
| 16. #5125 | C22 | semidirect |
| 21. C3×#349 | C22 | semidirect |
| 23. #4513 | C22 | semidirect |
| 29. #2115 | D3 | semidirect |
| 74. #349 | C2×D3 | semidirect |
| 255. C3 | #33657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83799 | 2 |
| #83789 | 2 |
| C3×#2115 | 2 |
| C2×#4516 | 2 |
| #71427 | 2 |
| #69116 | 2 |
| #33657 | 3 |