Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
658 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 103 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. #83314 | C2 | semidirect |
| 3. #83179 | C2 | semidirect |
| 4. #71811 | C2 | semidirect |
| 5. #71759 | C2 | semidirect |
| 6. #70766 | C2 | semidirect |
| 7. #67746 | C2 | semidirect |
| 144. C2×Dic6 | D8 | semidirect |
| 445. C3 | #10242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3205 | 2 |
| #83314 | 2 |
| #83179 | 2 |
| #71811 | 2 |
| #71759 | 2 |
| #70766 | 2 |
| #67746 | 2 |
| #10242 | 3 |