Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
452 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 452 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×#1460 | C2 | semidirect |
| 3. #71605 | C2 | semidirect |
| 4. #70790 | C2 | semidirect |
| 5. #70772 | C2 | semidirect |
| 6. #70749 | C2 | semidirect |
| 7. #67738 | C2 | semidirect |
| 33. #1460 | D3 | semidirect |
| 375. C3 | #10465 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #82307 | 2 |
| C3×#1460 | 2 |
| #71605 | 2 |
| #70790 | 2 |
| #70772 | 2 |
| #70749 | 2 |
| #67738 | 2 |
| #10465 | 3 |