Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
642 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 111 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. C2×#5070 | C2 | semidirect |
| 3. #78538 | C2 | semidirect |
| 4. C3×#1965 | C2 | semidirect |
| 5. #70506 | C2 | semidirect |
| 6. #70498 | C2 | semidirect |
| 7. #67667 | C2 | semidirect |
| 33. #1965 | D3 | semidirect |
| 130. C3×M16 | D8 | semidirect |
| 266. M16 | #213 | semidirect |
| 370. C3 | #10168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83166 | 2 |
| C2×#5070 | 2 |
| #78538 | 2 |
| C3×#1965 | 2 |
| #70506 | 2 |
| #70498 | 2 |
| #67667 | 2 |
| #10168 | 3 |