Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
392 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 97 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×#4565 | C2 | semidirect |
| 3. C2×#4564 | C2 | semidirect |
| 6. C2×#4493 | C2 | semidirect |
| 7. #67732 | C2 | semidirect |
| 320. C3 | #13394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#473 | 2 |
| C2×#4565 | 2 |
| C2×#4564 | 2 |
| #72016 | 2 |
| #72004 | 2 |
| C2×#4493 | 2 |
| #67732 | 2 |
| #13394 | 3 |