Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
404 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 93 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×#4563 | C2 | semidirect |
| 3. #72033 | C2 | semidirect |
| 4. #72013 | C2 | semidirect |
| 5. #72007 | C2 | semidirect |
| 6. #70685 | C2 | semidirect |
| 7. #67733 | C2 | semidirect |
| 320. C3 | #13402 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#472 | 2 |
| C2×#4563 | 2 |
| #72033 | 2 |
| #72013 | 2 |
| #72007 | 2 |
| #70685 | 2 |
| #67733 | 2 |
| #13402 | 3 |