Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
492 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 101 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. #71759 | C2 | semidirect |
| 3. #71759 | C2 | semidirect |
| 4. #71617 | C2 | semidirect |
| 5. #71597 | C2 | semidirect |
| 6. #70422 | C2 | semidirect |
| 7. #67707 | C2 | semidirect |
| 359. C3 | #10440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#459 | 2 |
| #71759 | 2 |
| #71617 | 2 |
| #71597 | 2 |
| #70422 | 2 |
| #67707 | 2 |
| #10440 | 3 |