Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
472 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 1. C3×#2971 | C2 | semidirect |
| 3. #71643 | C2 | semidirect |
| 4. #70832 | C2 | semidirect |
| 5. #69859 | C2 | semidirect |
| 6. #67754 | C2 | semidirect |
| 7. #67665 | C2 | semidirect |
| 20. #5027 | C4 | semidirect |
| 22. #5020 | C4 | semidirect |
| 23. #5015 | C4 | semidirect |
| 25. #5007 | C4 | semidirect |
| 35. #2971 | D3 | semidirect |
| 398. C3 | #9162 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2971 | 2 |
| #82531 | 2 |
| #71643 | 2 |
| #70832 | 2 |
| #69859 | 2 |
| #67754 | 2 |
| #67665 | 2 |
| #9162 | 3 |