Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
548 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 105 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. #74160 | C2 | semidirect |
| 3. C3×#1517 | C2 | semidirect |
| 4. #71811 | C2 | semidirect |
| 5. #70757 | C2 | semidirect |
| 6. #67746 | C2 | semidirect |
| 7. #67631 | C2 | semidirect |
| 15. #5083 | C4 | semidirect |
| 16. #5072 | C4 | semidirect |
| 32. #1517 | D3 | semidirect |
| 411. C3 | #9181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83297 | 2 |
| #74160 | 2 |
| C3×#1517 | 2 |
| #71811 | 2 |
| #70757 | 2 |
| #67746 | 2 |
| #67631 | 2 |
| #9181 | 3 |