Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
642 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 109 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. #83288 | C2 | semidirect |
| 3. C2×#5070 | C2 | semidirect |
| 4. #71802 | C2 | semidirect |
| 5. #71766 | C2 | semidirect |
| 6. #70778 | C2 | semidirect |
| 7. #67739 | C2 | semidirect |
| 146. #208 | D8 | semidirect |
| 370. C3 | #10168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3205 | 2 |
| #83288 | 2 |
| C2×#5070 | 2 |
| #71802 | 2 |
| #71766 | 2 |
| #70778 | 2 |
| #67739 | 2 |
| #10168 | 3 |