Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
408 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 408 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 |
|---|---|---|
| 2. C3×#1548 | C2 | semidirect |
| 3. #71775 | C2 | semidirect |
| 6. #70494 | C2 | semidirect |
| 7. #67745 | C2 | semidirect |
| 30. #1548 | D3 | semidirect |
| 316. C3 | #10449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5087 | 2 |
| C3×#1548 | 2 |
| #71775 | 2 |
| #70757 | 2 |
| #70527 | 2 |
| #70494 | 2 |
| #67745 | 2 |
| #10449 | 3 |