Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
492 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 97 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×#1571 | C2 | semidirect |
| 3. #70774 | C2 | semidirect |
| 4. #70756 | C2 | semidirect |
| 5. #70527 | C2 | semidirect |
| 6. #70502 | C2 | semidirect |
| 7. #67707 | C2 | semidirect |
| 28. #1571 | D3 | semidirect |
| 359. C3 | #10440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4843 | 2 |
| C3×#1571 | 2 |
| #70774 | 2 |
| #70756 | 2 |
| #70527 | 2 |
| #70502 | 2 |
| #67707 | 2 |
| #10440 | 3 |