Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
304 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 87 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. #70742 | C2 | semidirect |
| 4. #70495 | C2 | semidirect |
| 6. C3×#1299 | C2 | semidirect |
| 7. #67667 | C2 | semidirect |
| 33. #1299 | D3 | semidirect |
| 291. C3 | #9588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #70773 | 2 |
| #70742 | 2 |
| #70498 | 2 |
| #70495 | 2 |
| #69853 | 2 |
| C3×#1299 | 2 |
| #67667 | 2 |
| #9588 | 3 |