Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
312 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 89 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. #70753 | C2 | semidirect |
| 5. #69724 | C2 | semidirect |
| 6. C3×#1278 | C2 | semidirect |
| 7. #67669 | C2 | semidirect |
| 34. #1278 | D3 | semidirect |
| 291. C3 | #9586 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #70773 | 2 |
| #70753 | 2 |
| #69853 | 2 |
| #69735 | 2 |
| #69724 | 2 |
| C3×#1278 | 2 |
| #67669 | 2 |
| #9586 | 3 |