Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
456 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 3. C3×#1528 | C2 | semidirect |
| 4. #71737 | C2 | semidirect |
| 6. #67755 | C2 | semidirect |
| 7. #67668 | C2 | semidirect |
| 36. #1528 | D3 | semidirect |
| 399. C3 | #9245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5066 | 2 |
| #79336 | 2 |
| C3×#1528 | 2 |
| #71737 | 2 |
| #69855 | 2 |
| #67755 | 2 |
| #67668 | 2 |
| #9245 | 3 |