Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
470 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 123 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. #83780 | C2 | semidirect |
| 3. C3×#1812 | C2 | semidirect |
| 4. #70656 | C2 | semidirect |
| 5. #67726 | C2 | semidirect |
| 13. #5137 | C4 | semidirect |
| 14. #5135 | C4 | semidirect |
| 25. #1812 | D3 | semidirect |
| 56. #812 | D4 | semidirect |
| 271. C3 | #13077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83800 | 2 |
| #83780 | 2 |
| C3×#1812 | 2 |
| #70656 | 2 |
| #67726 | 2 |
| #13077 | 3 |