Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
424 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 91 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. #83127 | C2 | semidirect |
| 3. C3×#1521 | C2 | semidirect |
| 4. #70761 | C2 | semidirect |
| 5. #69564 | C2 | semidirect |
| 6. #67747 | C2 | semidirect |
| 7. #67633 | C2 | semidirect |
| 13. #5069 | C4 | semidirect |
| 14. #5067 | C4 | semidirect |
| 15. #5060 | C4 | semidirect |
| 16. #5058 | C4 | semidirect |
| 38. #1521 | D3 | semidirect |
| 402. C3 | #9370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83147 | 2 |
| #83127 | 2 |
| C3×#1521 | 2 |
| #70761 | 2 |
| #69564 | 2 |
| #67747 | 2 |
| #67633 | 2 |
| #9370 | 3 |