Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
614 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 614 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 1. C2×#5191 | C2 | semidirect |
| 2. C22×#828 | C2 | semidirect |
| 4. C2×C3×#358 | C2 | semidirect |
| 5. #70628 | C2 | semidirect |
| 6. C2×#4491 | C2 | semidirect |
| 7. #67804 | C2 | semidirect |
| 33. C2×#358 | D3 | semidirect |
| 391. C3 | #13326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5191 | 2 |
| C22×#828 | 2 |
| C22×D48 | 2 |
| C2×C3×#358 | 2 |
| #70628 | 2 |
| C2×#4491 | 2 |
| #67804 | 2 |
| #13326 | 3 |