Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
412 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 412 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. C3×#2165 | C2 | semidirect |
| 3. #69864 | C2 | semidirect |
| 4. #67571 | C2 | semidirect |
| 5. #67570 | C2 | semidirect |
| 18. C3×#364 | C22 | semidirect |
| 23. #4463 | C22 | semidirect |
| 26. #2165 | D3 | semidirect |
| 72. #364 | C2×D3 | semidirect |
| 292. C3 | #11992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78530 | 2 |
| C3×#2165 | 2 |
| #69864 | 2 |
| #67571 | 2 |
| #67570 | 2 |
| #11992 | 3 |