Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
514 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 101 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. #69862 | C2 | semidirect |
| 5. #69738 | C2 | semidirect |
| 6. C3×#1278 | C2 | semidirect |
| 7. #67743 | C2 | semidirect |
| 40. #1278 | D3 | semidirect |
| 399. C3 | #9212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79302 | 2 |
| C4×#901 | 2 |
| #69862 | 2 |
| #69854 | 2 |
| #69738 | 2 |
| C3×#1278 | 2 |
| #67743 | 2 |
| #9212 | 3 |