Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
442 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 79 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. #69106 | C2 | semidirect |
| 3. #68939 | C2 | semidirect |
| 4. C3×#1349 | C2 | semidirect |
| 5. #67775 | C2 | semidirect |
| 6. #67527 | C2 | semidirect |
| 7. #67487 | C2 | semidirect |
| 23. C3×C22⋊C16 | C22 | semidirect |
| 24. C3×#341 | C22 | semidirect |
| 25. #4552 | C22 | semidirect |
| 26. #4549 | C22 | semidirect |
| 34. #1349 | D3 | semidirect |
| 88. C22⋊C16 | C2×D3 | semidirect |
| 90. #341 | C2×D3 | semidirect |
| 368. C3 | #11895 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×#466 | 2 |
| #69106 | 2 |
| #68939 | 2 |
| C3×#1349 | 2 |
| #67775 | 2 |
| #67527 | 2 |
| #67487 | 2 |
| #11895 | 3 |