Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
394 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 77 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×#1350 | C2 | semidirect |
| 5. #67777 | C2 | semidirect |
| 6. #67527 | C2 | semidirect |
| 7. #67487 | C2 | semidirect |
| 32. #1350 | D3 | semidirect |
| 349. C3 | #11894 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #80758 | 2 |
| #69106 | 2 |
| #68939 | 2 |
| C3×#1350 | 2 |
| #67777 | 2 |
| #67527 | 2 |
| #67487 | 2 |
| #11894 | 3 |